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Risks, Volume 7, Issue 1 (March 2019)

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Open AccessArticle Mortality Forecasting: How Far Back Should We Look in Time?
Risks 2019, 7(1), 22; https://doi.org/10.3390/risks7010022 (registering DOI)
Received: 26 November 2018 / Revised: 2 February 2019 / Accepted: 19 February 2019 / Published: 22 February 2019
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Abstract
Extrapolative methods are one of the most commonly-adopted forecasting approaches in the literature on projecting future mortality rates. It can be argued that there are two types of mortality models using this approach. The first extracts patterns in age, time and cohort dimensions [...] Read more.
Extrapolative methods are one of the most commonly-adopted forecasting approaches in the literature on projecting future mortality rates. It can be argued that there are two types of mortality models using this approach. The first extracts patterns in age, time and cohort dimensions either in a deterministic fashion or a stochastic fashion. The second uses non-parametric smoothing techniques to model mortality and thus has no explicit constraints placed on the model. We argue that from a forecasting point of view, the main difference between the two types of models is whether they treat recent and historical information equally in the projection process. In this paper, we compare the forecasting performance of the two types of models using Great Britain male mortality data from 1950–2016. We also conduct a robustness test to see how sensitive the forecasts are to the changes in the length of historical data used to calibrate the models. The main conclusion from the study is that more recent information should be given more weight in the forecasting process as it has greater predictive power over historical information. Full article
Open AccessArticle An Indexation Mechanism for Retirement Age: Analysis of the Gender Gap
Risks 2019, 7(1), 21; https://doi.org/10.3390/risks7010021 (registering DOI)
Received: 29 November 2018 / Revised: 8 February 2019 / Accepted: 8 February 2019 / Published: 22 February 2019
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Abstract
The management of National Social Security Systems is being challenged more and more by the rapid ageing of the population, especially in the industrialized countries. In order to chase the Pension System sustainability, several countries in Europe are setting up pension reforms linking [...] Read more.
The management of National Social Security Systems is being challenged more and more by the rapid ageing of the population, especially in the industrialized countries. In order to chase the Pension System sustainability, several countries in Europe are setting up pension reforms linking the retirement age and/or benefits to life expectancy. In this context, the accurate modelling and projection of mortality rates and life expectancy play a central role and represent issues of great interest in recent literature. Our study refers to the Italian mortality experience and considers an indexing mechanism based on the expected residual life to adjust the retirement age and keep costs at an expected budgeted level, in the spirit of sharing the longevity risk between Social Security Systems and retirees. In order to combine fitting and projections performances of selected stochastic mortality models, a model assembling technique is applied to face uncertainty in model selection, while accounting for uncertainty of estimation as well. The resulting proposal is an averaged model that is suitable to discuss about the gender gap in longevity risk and its alleged narrowing over time. Full article
(This article belongs to the Special Issue New Perspectives in Actuarial Risk Management)
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Open AccessArticle Market Risk and Financial Performance of Non-Financial Companies Listed on the Moroccan Stock Exchange
Received: 17 January 2019 / Revised: 17 February 2019 / Accepted: 18 February 2019 / Published: 21 February 2019
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Abstract
This study examines the effect of market risk on the financial performance of 31 non-financial companies listed on the Casablanca Stock Exchange (CSE) over the period 2000–2016. We utilized three alternative variables to assess financial performance, namely, the return on assets, the return [...] Read more.
This study examines the effect of market risk on the financial performance of 31 non-financial companies listed on the Casablanca Stock Exchange (CSE) over the period 2000–2016. We utilized three alternative variables to assess financial performance, namely, the return on assets, the return on equity and the profit margin. We used the degree of financial leverage, the book-to-market ratio, and the gearing ratio as the indicators of market risk. Then, we employed the pooled OLS model, the fixed effects model, the random effects model, the difference-GMM and the system-GMM models. The results show that the different measures of market risk have significant negative influences on the companies’ financial performance. The elasticities are greater following the degree of financial leverage compared with the book-to-market ratio and the gearing ratio. In most cases, the firm’s age, the cash holdings ratio, the firm’s size, the debt-to-assets ratio, and the tangibility ratio have positive effects on financial performance, whereas the debt-to-income ratio and the stock turnover hurt the performance of these non-financial companies. Therefore, decision-makers and managers should mitigate market risk through appropriate strategies of risk management, such as derivatives and insurance techniques. Full article
Open AccessArticle Modelling Recovery Rates for Non-Performing Loans
Received: 12 February 2019 / Accepted: 15 February 2019 / Published: 20 February 2019
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Abstract
Based on a rich dataset of recoveries donated by a debt collection business, recovery rates for non-performing loans taken from a single European country are modelled using linear regression, linear regression with Lasso, beta regression and inflated beta regression. We also propose a [...] Read more.
Based on a rich dataset of recoveries donated by a debt collection business, recovery rates for non-performing loans taken from a single European country are modelled using linear regression, linear regression with Lasso, beta regression and inflated beta regression. We also propose a two-stage model: beta mixture model combined with a logistic regression model. The proposed model allowed us to model the multimodal distribution we found for these recovery rates. All models were built using loan characteristics, default data and collections data prior to purchase by the debt collection business. The intended use of the models was to estimate future recovery rates for improved risk assessment, capital requirement calculations and bad debt management. They were compared using a range of quantitative performance measures under K-fold cross validation. Among all the models, we found that the proposed two-stage beta mixture model performs best. Full article
(This article belongs to the Special Issue Advances in Credit Risk Modeling and Management)
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Open AccessArticle The W,Z/ν,δ Paradigm for the First Passage of Strong Markov Processes without Positive Jumps
Received: 21 November 2018 / Revised: 31 January 2019 / Accepted: 13 February 2019 / Published: 19 February 2019
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Abstract
As is well-known, the benefit of restricting Lévy processes without positive jumps is the “W,Z scale functions paradigm”, by which the knowledge of the scale functions W,Z extends immediately to other risk control problems. The same is true [...] Read more.
As is well-known, the benefit of restricting Lévy processes without positive jumps is the “ W , Z scale functions paradigm”, by which the knowledge of the scale functions W , Z extends immediately to other risk control problems. The same is true largely for strong Markov processes X t , with the notable distinctions that (a) it is more convenient to use as “basis” differential exit functions ν , δ , and that (b) it is not yet known how to compute ν , δ or W , Z beyond the Lévy, diffusion, and a few other cases. The unifying framework outlined in this paper suggests, however, via an example that the spectrally negative Markov and Lévy cases are very similar (except for the level of work involved in computing the basic functions ν , δ ). We illustrate the potential of the unified framework by introducing a new objective () for the optimization of dividends, inspired by the de Finetti problem of maximizing expected discounted cumulative dividends until ruin, where we replace ruin with an optimally chosen Azema-Yor/generalized draw-down/regret/trailing stopping time. This is defined as a hitting time of the “draw-down” process Y t = sup 0 s t X s - X t obtained by reflecting X t at its maximum. This new variational problem has been solved in a parallel paper. Full article
Open AccessArticle Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits
Received: 11 December 2018 / Revised: 31 January 2019 / Accepted: 4 February 2019 / Published: 11 February 2019
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Abstract
Phase-type (PH) distributions are defined as distributions of lifetimes of finite continuous-time Markov processes. Their traditional applications are in queueing, insurance risk, and reliability, but more recently, also in finance and, though to a lesser extent, to life and health insurance. The advantage [...] Read more.
Phase-type (PH) distributions are defined as distributions of lifetimes of finite continuous-time Markov processes. Their traditional applications are in queueing, insurance risk, and reliability, but more recently, also in finance and, though to a lesser extent, to life and health insurance. The advantage is that PH distributions form a dense class and that problems having explicit solutions for exponential distributions typically become computationally tractable under PH assumptions. In the first part of this paper, fitting of PH distributions to human lifetimes is considered. The class of generalized Coxian distributions is given special attention. In part, some new software is developed. In the second part, pricing of life insurance products such as guaranteed minimum death benefit and high-water benefit is treated for the case where the lifetime distribution is approximated by a PH distribution and the underlying asset price process is described by a jump diffusion with PH jumps. The expressions are typically explicit in terms of matrix-exponentials involving two matrices closely related to the Wiener-Hopf factorization, for which recently, a Lévy process version has been developed for a PH horizon. The computational power of the method of the approach is illustrated via a number of numerical examples. Full article
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Open AccessArticle Pricing Options and Computing Implied Volatilities using Neural Networks
Received: 8 January 2019 / Revised: 3 February 2019 / Accepted: 6 February 2019 / Published: 9 February 2019
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Abstract
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized [...] Read more.
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly. Full article
Open AccessReview Can Sustainable Investment Yield Better Financial Returns: A Comparative Study of ESG Indices and MSCI Indices
Received: 24 December 2018 / Revised: 22 January 2019 / Accepted: 29 January 2019 / Published: 2 February 2019
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Abstract
‘Sustainable investment’—includes a variety of asset classes selected while caring for the causes of environmental, social, and governance (ESG). It is an investment strategy that seeks to combine social and/ or environmental benefits with financial returns, thus linking investor’s social, ethical, ecological and [...] Read more.
‘Sustainable investment’—includes a variety of asset classes selected while caring for the causes of environmental, social, and governance (ESG). It is an investment strategy that seeks to combine social and/ or environmental benefits with financial returns, thus linking investor’s social, ethical, ecological and economic concerns Under certain conditions, these indices also help to attract foreign capital, seeking international participation in the local capital markets. The purpose of this paper is to study whether the sustainable investment alternatives offer better financial returns than the conventional indices from both developed and emerging markets. With an intent to maintain consistency, this paper comparatively analyzes the financial returns of the Thomson Reuters/S-Network global indices, namely the developed markets (excluding US) ESG index—TRESGDX, emerging markets ESG index—TRESGEX, US large-cap ESG index—TRESGUS, Europe ESG index—TRESGEU, and those of the usual markets, namely MSCI world index (MSCI W), MSCI All Country World Equity index (MSCI ACWI), MSCI USA index (MSCI USA), and MSCI Europe Australasia Far East index (MSCI EAFE), MSCI Emerging Markets index (MSCI EM) and MSCI Europe index (MSCI EU). The study also focusses on the inter-linkages between these indices. Daily closing prices of all the benchmark indices are taken for the five-year period of January 2013–December 2017. Line charts and unit-root tests are applied to check the stationary nature of the series; Granger’s causality model, auto-regressive conditional heteroskedasticity (ARCH)-GARCH type modelling is performed to find out the linkages between the markets under study followed by the Johansen’s cointegration test and the Vector Error Correction Model to test the volatility spillover between the sustainable indices and the conventional indices. The study finds that the sustainable indices and the conventional indices are integrated and there is a flow of information between the two investment avenues. The results indicate that there is no significant difference in the performance between sustainable indices and the traditional conventional indices, being a good substitute to the latter. Hence, the financial/investment managers can obtain more insights regarding investment decisions, and the study further suggests that their portfolios should consider both the indices with the perspective of diversifying the risk and hedging, and reap benefits of the same. Additionally, corporate executives shall use it to benchmark their own performance against peers and track news as well. Full article
Open AccessArticle Changes of Relation in Multi-Population Mortality Dependence: An Application of Threshold VECM
Received: 7 January 2019 / Revised: 26 January 2019 / Accepted: 28 January 2019 / Published: 1 February 2019
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Abstract
Standardized longevity risk transfers often involve modeling mortality rates of multiple populations. Some researchers have found that mortality indexes of selected countries are cointegrated, meaning that a linear relationship exists between the indexes. Vector error correction model (VECM) was used to incorporate this [...] Read more.
Standardized longevity risk transfers often involve modeling mortality rates of multiple populations. Some researchers have found that mortality indexes of selected countries are cointegrated, meaning that a linear relationship exists between the indexes. Vector error correction model (VECM) was used to incorporate this relation, thereby forcing the mortality rates of multiple populations to revert to a long-run equilibrium. However, the long-run equilibrium may change over time. It is crucial to incorporate these changes such that mortality dependence is adequately modeled. In this paper, we develop a framework to examine the presence of equilibrium changes and to incorporate these changes into the mortality model. In particular, we focus on equilibrium changes caused by threshold effect, the phenomenon that mortality indexes alternate between different VECMs depending on the value of a threshold variable. Our framework comprises two steps. In the first step, a statistical test is performed to examine the presence of threshold effect in the VECM for multiple mortality indexes. In the second step, threshold vector error correction model (TVECM) is fitted to the mortality indexes and model adequacy is evaluated. We illustrate this framework with the mortality data of England and Wales (EW) and Canadian populations. We further apply the TVECM to forecast future mortalities and price an illustrative longevity bond with multivariate Wang transform. Our numerical results show that TVECM predicted much faster mortality improvement for EW and Canada than single-regime VECM and thus the incorporation of threshold effect significant increases longevity bond price. Full article
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Open AccessArticle Optimal Bail-Out Dividend Problem with Transaction Cost and Capital Injection Constraint
Received: 18 December 2018 / Revised: 28 January 2019 / Accepted: 29 January 2019 / Published: 31 January 2019
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Abstract
We consider the optimal bail-out dividend problem with fixed transaction cost for a Lévy risk model with a constraint on the expected present value of injected capital. To solve this problem, we first consider the optimal bail-out dividend problem with transaction cost and [...] Read more.
We consider the optimal bail-out dividend problem with fixed transaction cost for a Lévy risk model with a constraint on the expected present value of injected capital. To solve this problem, we first consider the optimal bail-out dividend problem with transaction cost and capital injection and show the optimality of reflected ( c 1 , c 2 ) -policies. We then find the optimal Lagrange multiplier, by showing that in the dual Lagrangian problem the complementary slackness conditions are met. Finally, we present some numerical examples to support our results. Full article
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Open AccessArticle Measuring Equity Share Related Risk Perception of Investors in Economically Backward Regions
Received: 7 December 2018 / Revised: 14 January 2019 / Accepted: 14 January 2019 / Published: 30 January 2019
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Abstract
Risk perception is an idiosyncratic process of interpretation. It is a highly personal process of making a decision based on an individual’s frame of reference that has evolved over time. The purpose of this paper is to find out the risk perception level [...] Read more.
Risk perception is an idiosyncratic process of interpretation. It is a highly personal process of making a decision based on an individual’s frame of reference that has evolved over time. The purpose of this paper is to find out the risk perception level of equity investors and to identify the factors influencing their risk perception. The study was conducted using a stratified random sampling design of 358 investors. It was found that the overall risk perception level of equity investors is moderate and that the main factors affecting their risk perception are information screening, investment education, fear psychosis, fundamental expertise, technical expertise, familiarity bias, information asymmetry, understanding of the market, etc. Considering the above findings, efforts should be made to bring people with a high risk perception to the low risk perception category by providing them with training to handle or manage high-risk scenarios which will help in promoting an equity-investment culture. Full article
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Open AccessArticle Multivariate Risk-Neutral Pricing of Reverse Mortgages under the Bayesian Framework
Received: 16 December 2018 / Revised: 20 January 2019 / Accepted: 21 January 2019 / Published: 24 January 2019
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Abstract
In this paper, we suggest a Bayesian multivariate approach for pricing a reverse mortgage, allowing for house price risk, interest rate risk and longevity risk. We adopt the principle of maximum entropy in risk-neutralisation of these three risk components simultaneously. Our numerical results [...] Read more.
In this paper, we suggest a Bayesian multivariate approach for pricing a reverse mortgage, allowing for house price risk, interest rate risk and longevity risk. We adopt the principle of maximum entropy in risk-neutralisation of these three risk components simultaneously. Our numerical results based on Australian data suggest that a reverse mortgage would be financially sustainable under the current financial environment and the model settings and assumptions. Full article
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Open AccessArticle Risk Model Validation: An Intraday VaR and ES Approach Using the Multiplicative Component GARCH
Received: 12 December 2018 / Revised: 18 January 2019 / Accepted: 19 January 2019 / Published: 23 January 2019
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Abstract
In this paper, we employ 99% intraday value-at-risk (VaR) and intraday expected shortfall (ES) as risk metrics to assess the competency of the Multiplicative Component Generalised Autoregressive Heteroskedasticity (MC-GARCH) models based on the 1-min EUR/USD exchange rate returns. Five distributional assumptions for the [...] Read more.
In this paper, we employ 99% intraday value-at-risk (VaR) and intraday expected shortfall (ES) as risk metrics to assess the competency of the Multiplicative Component Generalised Autoregressive Heteroskedasticity (MC-GARCH) models based on the 1-min EUR/USD exchange rate returns. Five distributional assumptions for the innovation process are used to analyse their effects on the modelling and forecasting performance. The high-frequency volatility models were validated in terms of in-sample fit based on various statistical and graphical tests. A more rigorous validation procedure involves testing the predictive power of the models. Therefore, three backtesting procedures were used for the VaR, namely, the Kupiec’s test, a duration-based backtest, and an asymmetric VaR loss function. Similarly, three backtests were employed for the ES: a regression-based backtesting procedure, the Exceedance Residual backtest and the V-Tests. The validation results show that non-normal distributions are best suited for both model fitting and forecasting. The MC-GARCH(1,1) model under the Generalised Error Distribution (GED) innovation assumption gave the best fit to the intraday data and gave the best results for the ES forecasts. However, the asymmetric Skewed Student’s-t distribution for the innovation process provided the best results for the VaR forecasts. This paper presents the results of the first empirical study (to the best of the authors’ knowledge) in: (1) forecasting the intraday Expected Shortfall (ES) under different distributional assumptions for the MC-GARCH model; (2) assessing the MC-GARCH model under the Generalised Error Distribution (GED) innovation; (3) evaluating and ranking the VaR predictability of the MC-GARCH models using an asymmetric loss function. Full article
Open AccessArticle Efficient Retirement Portfolios: Using Life Insurance to Meet Income and Bequest Goals in Retirement
Received: 26 October 2018 / Revised: 21 December 2018 / Accepted: 4 January 2019 / Published: 18 January 2019
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Abstract
Life Insurance Retirement Plans (LIRPs) offer tax-deferred cash value accumulation, tax-free withdrawals (if properly structured), and a tax-free death benefit to beneficiaries. Thus, LIRPs share many of the tax advantages of other retirement savings vehicles but with less restrictive limitations on income and [...] Read more.
Life Insurance Retirement Plans (LIRPs) offer tax-deferred cash value accumulation, tax-free withdrawals (if properly structured), and a tax-free death benefit to beneficiaries. Thus, LIRPs share many of the tax advantages of other retirement savings vehicles but with less restrictive limitations on income and contributions. Opinions are mixed about the effectiveness of LIRPs; some financial advisers recommend them enthusiastically, while others are more skeptical. In this paper, we examine the potential of LIRPs to meet both income and bequest needs in retirement. We contrast retirement portfolios that include a LIRP with those that include only investment products with no life insurance. We consider different issue ages, face amounts, and withdrawal patterns. We simulate market scenarios and we demonstrate that portfolios that include LIRPs yield higher legacy potential and smaller income risk than those that exclude it. Thus, we conclude that the inclusion of a LIRP can improve financial outcomes in retirement. Full article
(This article belongs to the Special Issue Young Researchers in Insurance and Risk Management)
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Open AccessArticle An Object-Oriented Bayesian Framework for the Detection of Market Drivers
Received: 23 November 2018 / Revised: 3 January 2019 / Accepted: 4 January 2019 / Published: 14 January 2019
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Abstract
We use Object Oriented Bayesian Networks (OOBNs) to analyze complex ties in the equity market and to detect drivers for the Standard & Poor’s 500 (S&P 500) index. To such aim, we consider a vast number of indicators drawn from various investment areas [...] Read more.
We use Object Oriented Bayesian Networks (OOBNs) to analyze complex ties in the equity market and to detect drivers for the Standard & Poor’s 500 (S&P 500) index. To such aim, we consider a vast number of indicators drawn from various investment areas (Value, Growth, Sentiment, Momentum, and Technical Analysis), and, with the aid of OOBNs, we study the role they played along time in influencing the dynamics of the S&P 500. Our results highlight that the centrality of the indicators varies in time, and offer a starting point for further inquiries devoted to combine OOBNs with trading platforms. Full article
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Open AccessArticle Surplus Sharing with Coherent Utility Functions
Received: 2 November 2018 / Revised: 20 December 2018 / Accepted: 27 December 2018 / Published: 10 January 2019
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Abstract
We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting [...] Read more.
We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e., the shareholders. Full article
Open AccessArticle Convolutional Neural Network Classification of Telematics Car Driving Data
Received: 29 October 2018 / Revised: 21 December 2018 / Accepted: 9 January 2019 / Published: 10 January 2019
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Abstract
The aim of this project is to analyze high-frequency GPS location data (second per second) of individual car drivers (and trips). We extract feature information about speeds, acceleration, deceleration, and changes of direction from this high-frequency GPS location data. Time series of this [...] Read more.
The aim of this project is to analyze high-frequency GPS location data (second per second) of individual car drivers (and trips). We extract feature information about speeds, acceleration, deceleration, and changes of direction from this high-frequency GPS location data. Time series of this feature information allow us to appropriately allocate individual car driving trips to selected drivers using convolutional neural networks. Full article
(This article belongs to the Special Issue Insurance: Spatial and Network Data)
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Open AccessArticle Dealing with Drift Uncertainty: A Bayesian Learning Approach
Received: 20 November 2018 / Revised: 25 December 2018 / Accepted: 4 January 2019 / Published: 9 January 2019
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Abstract
One of the main challenges investors have to face is model uncertainty. Typically, the dynamic of the assets is modeled using two parameters: the drift vector and the covariance matrix, which are both uncertain. Since the variance/covariance parameter is assumed to be estimated [...] Read more.
One of the main challenges investors have to face is model uncertainty. Typically, the dynamic of the assets is modeled using two parameters: the drift vector and the covariance matrix, which are both uncertain. Since the variance/covariance parameter is assumed to be estimated with a certain level of confidence, we focus on drift uncertainty in this paper. Building on filtering techniques and learning methods, we use a Bayesian learning approach to solve the Markowitz problem and provide a simple and practical procedure to implement optimal strategy. To illustrate the value added of using the optimal Bayesian learning strategy, we compare it with an optimal nonlearning strategy that keeps the drift constant at all times. In order to emphasize the prevalence of the Bayesian learning strategy above the nonlearning one in different situations, we experiment three different investment universes: indices of various asset classes, currencies and smart beta strategies. Full article
(This article belongs to the Special Issue Applications of Stochastic Optimal Control to Economics and Finance)
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Open AccessEditorial Acknowledgement to Reviewers of Risks in 2018
Received: 8 January 2019 / Accepted: 8 January 2019 / Published: 8 January 2019
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Abstract
Rigorous peer-review is the corner-stone of high-quality academic publishing. [...] Full article
Open AccessArticle Bail-In or Bail-Out? Correlation Networks to Measure the Systemic Implications of Bank Resolution
Received: 28 November 2018 / Revised: 22 December 2018 / Accepted: 27 December 2018 / Published: 5 January 2019
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Abstract
We propose a statistical measure, based on correlation networks, to evaluate the systemic risk that could arise from the resolution of a failing or likely-to-fail financial institution, under three alternative scenarios: liquidation, private recapitalization, or bail-in. The measure enhances the observed CDS spreads [...] Read more.
We propose a statistical measure, based on correlation networks, to evaluate the systemic risk that could arise from the resolution of a failing or likely-to-fail financial institution, under three alternative scenarios: liquidation, private recapitalization, or bail-in. The measure enhances the observed CDS spreads with a risk premium that derives from contagion effects across financial institutions. The empirical findings reveal that the recapitalization of a distressed bank performed by the other banks in the system and the bail-in resolution minimize the potential losses for the banking sector with respect to the liquidation scenario, thus posing limited systemic risks. A closer comparison between the private intervention recapitalization and the bail-in tool shows that the latter slightly reduces contagion effects with respect to the private intervention scenario. Full article
(This article belongs to the Special Issue Model Risk in Finance)
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Open AccessArticle Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives
Received: 27 November 2018 / Revised: 20 December 2018 / Accepted: 22 December 2018 / Published: 3 January 2019
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Abstract
This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap for a life annuity portfolio. Although longevity swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, provide more effective downside [...] Read more.
This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap for a life annuity portfolio. Although longevity swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, provide more effective downside protection. A tractable stochastic mortality model with age dependent drift and volatility is developed and analytical formulae for prices of longevity derivatives are derived. The model is calibrated using Australian mortality data. The hedging of the life annuity portfolio is comprehensively assessed for a range of assumptions for the longevity risk premium, the term to maturity of the hedging instruments, as well as the size of the underlying annuity portfolio. The results compare the risk management benefits and costs of longevity derivatives with linear and nonlinear payoff structures. Full article
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Open AccessArticle Using Neural Networks to Price and Hedge Variable Annuity Guarantees
Received: 1 November 2018 / Revised: 28 November 2018 / Accepted: 20 December 2018 / Published: 23 December 2018
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Abstract
This paper explores the use of neural networks to reduce the computational cost of pricing and hedging variable annuity guarantees. Pricing these guarantees can take a considerable amount of time because of the large number of Monte Carlo simulations that are required for [...] Read more.
This paper explores the use of neural networks to reduce the computational cost of pricing and hedging variable annuity guarantees. Pricing these guarantees can take a considerable amount of time because of the large number of Monte Carlo simulations that are required for the fair value of these liabilities to converge. This computational requirement worsens when Greeks must be calculated to hedge the liabilities of these guarantees. A feedforward neural network is a universal function approximator that is proposed as a useful machine learning technique to interpolate between previously calculated values and avoid running a full simulation to obtain a value for the liabilities. We propose methodologies utilizing neural networks for both the tasks of pricing as well as hedging four different varieties of variable annuity guarantees. We demonstrated a significant efficiency gain using neural networks in this manner. We also experimented with different error functions in the training of the neural networks and examined the resulting changes in network performance. Full article
(This article belongs to the Special Issue Young Researchers in Insurance and Risk Management)
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