Open AccessArticle
Dread Disease and Cause-Specific Mortality: Exploring New Forms of Insured Loans
Risks 2018, 6(1), 13; doi:10.3390/risks6010013 (registering DOI) -
Abstract
The relevance of critical illness coverage and life insurance in cause-specific mortality conditions is increasing in many industrialized countries. Specific conditions on the illness and on death event, providing cheapest premiums for the insureds and lower obligations for the insurers, constitute interesting products
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The relevance of critical illness coverage and life insurance in cause-specific mortality conditions is increasing in many industrialized countries. Specific conditions on the illness and on death event, providing cheapest premiums for the insureds and lower obligations for the insurers, constitute interesting products in an insurance market looking to offer appealing products. On the other hand, the systematic improvement in longevity gives rise to a market with agents getting increasingly older, and the insurer pays attention to this trend. There are financial contracts joined with insurance coverage, and this particularly happens in the case of the so-called insured loan. Insured loans are financial contracts often proposed together with a term life insurance in order to cover the lender and the heirs against the borrower’s death event within the loan duration. This paper explores new insurance products that, linked to an insured loan, are founded on specific illness hypotheses and/or cause-specific mortality. The aim is to value how much the insurance costs lighten with respect to the traditional term insurance. The authors project cause-specific mortality rates and specific diagnosis rates, in this last case overcoming the discontinuities in the data. The new contractual schemes are priced. Numerical applications also show, with several graphs, the rates projection procedure and plenty of tables report the premiums in the new proposed contractual forms. The complete amortization schedule closes the work. Full article
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Open AccessArticle
Stable Value Funds Performance
Risks 2018, 6(1), 12; doi:10.3390/risks6010012 -
Abstract
Little in the scholarly economics literature is directed specifically to the performance of stable value funds, although they occupy a leading place among retirement investment vehicles. They are currently offered in more than one-third of all defined contribution plans in the USA, with
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Little in the scholarly economics literature is directed specifically to the performance of stable value funds, although they occupy a leading place among retirement investment vehicles. They are currently offered in more than one-third of all defined contribution plans in the USA, with more than $800 billion of assets under management. This paper rigorously examines their performance throughout the entire period since their inception in 1973. We produce a composite index of stable value returns. We next conduct mean-variance analysis, Sharpe and Sortino ratio analysis, stochastic dominance analysis, and optimal multi-period portfolio composition analysis. Our evidence suggests that stable value funds dominate (on average) two major asset classes based on a historical analysis, and that they often occupy a significant position in optimized portfolios across a broad range of risk aversion levels. We discuss factors that contributed to stable value funds’ past performance and whether they can continue to perform well into the future. We also discuss considerations regarding whether or not to include stable value as an element in target date funds within defined contribution pension plans. Full article
Open AccessArticle
A Note on Parameter Estimation in the Composite Weibull–Pareto Distribution
Risks 2018, 6(1), 11; doi:10.3390/risks6010011 -
Abstract
Composite models have received much attention in the recent actuarial literature to describe heavy-tailed insurance loss data. One of the models that presents a good performance to describe this kind of data is the composite Weibull–Pareto (CWL) distribution. On this note, this distribution
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Composite models have received much attention in the recent actuarial literature to describe heavy-tailed insurance loss data. One of the models that presents a good performance to describe this kind of data is the composite Weibull–Pareto (CWL) distribution. On this note, this distribution is revisited to carry out estimation of parameters via mle and mle2 optimization functions in R. The results are compared with those obtained in a previous paper by using the nlm function, in terms of analytical and graphical methods of model selection. In addition, the consistency of the parameter estimation is examined via a simulation study. Full article
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Open AccessArticle
Longevity Risk Management and the Development of a Value-Based Longevity Index
Risks 2018, 6(1), 10; doi:10.3390/risks6010010 -
Abstract
The design and development of post-retirement income products require the assessment of longevity risk, as well as a basis for hedging these risks. Most indices for longevity risk are age-period based. We develop and assess a cohort-based value index for life insurers and
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The design and development of post-retirement income products require the assessment of longevity risk, as well as a basis for hedging these risks. Most indices for longevity risk are age-period based. We develop and assess a cohort-based value index for life insurers and pension funds to manage longevity risk. There are two innovations in the development of this index. Firstly, the underlying variables of most existing longevity indices are based on mortality experience only. The value index is based on the present value of future cash flow obligations, capturing all the risks in retirement income products. We use the index to manage both longevity risk and interest rate risk. Secondly, we capture historical dependencies between ages and cohorts with a cohort-based stochastic mortality model. We achieve this by introducing age-dependent model parameters. With our mortality model, we obtain realistic cohort correlation structures and improve the fitting performance, particularly for very old ages. Full article
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Open AccessArticle
Health Care Workers’ Risk Perceptions and Willingness to Report for Work during an Influenza Pandemic
Risks 2018, 6(1), 8; doi:10.3390/risks6010008 -
Abstract
The ability and willingness of health care workers to report for work during a pandemic are essential to pandemic response. The main contribution of this article is to examine the relationship between risk perception of personal and work activities and willingness to report
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The ability and willingness of health care workers to report for work during a pandemic are essential to pandemic response. The main contribution of this article is to examine the relationship between risk perception of personal and work activities and willingness to report for work during an influenza pandemic. Data were collected through a quantitative Web-based survey sent to health care workers on the island of Montreal. Respondents were asked about their perception of various risks to obtain index measures of risk perception. A multinomial logit model was applied for the probability estimations, and a factor analysis was conducted to compute risk perception indexes (scores). Risk perception associated with personal and work activities is a significant predictor of intended presence at work during an influenza pandemic. This means that correcting perceptual biases should be a public policy concern. These results have not been previously reported in the literature. Many organizational variables are also significant. Full article
Open AccessFeature PaperArticle
Price and Profit Optimization for Financial Services
Risks 2018, 6(1), 9; doi:10.3390/risks6010009 -
Abstract
Prospective customers of financial and insurance products can be targeted based on the profit the provider expects to earn from them. We present a model for individual expected profit and two alternatives for calculating optimal personalized prices that maximize the expected profit. For
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Prospective customers of financial and insurance products can be targeted based on the profit the provider expects to earn from them. We present a model for individual expected profit and two alternatives for calculating optimal personalized prices that maximize the expected profit. For one of these alternatives, we obtain a closed-form expression for the price offered to each prospective customer; for the other, we need to use a numerical approximation. In both approaches, the profits generated by prospective customers are not immediately observed, given that the products sold by these companies have a risk component. We assume that willingness to pay is heterogeneous and apply our methodology using real data from a European insurance company. Our study indicates that a substantial boost in profits can be expected when applying the simplest optimal pricing method proposed. Full article
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Open AccessArticle
Financial Time Series Forecasting Using Empirical Mode Decomposition and Support Vector Regression
Risks 2018, 6(1), 7; doi:10.3390/risks6010007 -
Abstract
We introduce a multistep-ahead forecasting methodology that combines empirical mode decomposition (EMD) and support vector regression (SVR). This methodology is based on the idea that the forecasting task is simplified by using as input for SVR the time series decomposed with EMD. The
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We introduce a multistep-ahead forecasting methodology that combines empirical mode decomposition (EMD) and support vector regression (SVR). This methodology is based on the idea that the forecasting task is simplified by using as input for SVR the time series decomposed with EMD. The outcomes of this methodology are compared with benchmark models commonly used in the literature. The results demonstrate that the combination of EMD and SVR can outperform benchmark models significantly, predicting the Standard & Poor’s 500 Index from 30 s to 25 min ahead. The high-frequency components better forecast short-term horizons, whereas the low-frequency components better forecast long-term horizons. Full article
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Open AccessArticle
On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends
Risks 2018, 6(1), 6; doi:10.3390/risks6010006 -
Abstract
This paper extends the work of Yuen et al. (2013), who obtained explicit results for the discount-free Gerber–Shiu function for a compound binomial risk model in the presence of delayed claims and a randomized dividend strategy with a zero threshold level. Specifically, we
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This paper extends the work of Yuen et al. (2013), who obtained explicit results for the discount-free Gerber–Shiu function for a compound binomial risk model in the presence of delayed claims and a randomized dividend strategy with a zero threshold level. Specifically, we establish a recursion method for computing the Gerber–Shiu expected discounted penalty function, which entails a number of important quantities in ruin theory, within the framework of the compound binomial aggregate claims with delayed by-claims and randomized dividends payable at a non-negative threshold level. Full article
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Open AccessFeature PaperArticle
Optimal Investment under Cost Uncertainty
Risks 2018, 6(1), 5; doi:10.3390/risks6010005 -
Abstract
This paper studies the valuation of real options when the cost of investment jumps at a random time. Three valuation formulas are derived. The first expresses the value of the project in terms of a collection of knockout barrier claims. The second identifies
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This paper studies the valuation of real options when the cost of investment jumps at a random time. Three valuation formulas are derived. The first expresses the value of the project in terms of a collection of knockout barrier claims. The second identifies the premium relative to a project with delayed investment right and prices its components. The last one identifies the premium/discount relative to a project with constant cost equal to the post-jump cost and prices its components. All formulas are in closed form. The behavior of optimal investment boundaries and valuation components are examined. Full article
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Open AccessEditorial
Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance
Risks 2018, 6(1), 4; doi:10.3390/risks6010004 -
Abstract
In the nearly thirty years since Hans Buhlmann (Buhlmann (1987)) set out the notion of the Actuary of the Third Kind, the connection between Actuarial Science (AS) and Mathematical Finance (MF) has been continually reinforced. As siblings in the family of Risk Management
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In the nearly thirty years since Hans Buhlmann (Buhlmann (1987)) set out the notion of the Actuary of the Third Kind, the connection between Actuarial Science (AS) and Mathematical Finance (MF) has been continually reinforced. As siblings in the family of Risk Management techniques, practitioners in both fields have learned a great deal from each other. The collection of articles in this volume are contributed by scholars who are not only experts in areas of AS and MF, but also those who present diverse perspectives from both industry and academia. Topics from multiple areas, such as Stochastic Modeling, Credit Risk, Monte Carlo Simulation, and Pension Valuation, among others, that were maybe thought to be the domain of one type of risk manager are shown time and again to have deep value to other areas of risk management as well. The articles in this collection, in my opinion, contribute techniques, ideas, and overviews of tools that specialists in both AS and MF will find useful and interesting to implement in their work. It is also my hope that this collection will inspire future collaboration between those who seek an interdisciplinary approach to risk management. Full article
Open AccessEditorial
Acknowledgement to Reviewers of Risks in 2017
Risks 2018, 6(1), 3; doi:10.3390/risks6010003 -
Open AccessArticle
A Simple Traffic Light Approach to Backtesting Expected Shortfall
Risks 2018, 6(1), 2; doi:10.3390/risks6010002 -
Abstract
We propose a Traffic Light approach to backtesting Expected Shortfall which is completely consistent with, and analogous to, the Traffic Light approach to backtesting VaR (Value at Risk) initially proposed by the Basel Committee on Banking Supervision in their 1996 consultative document Basle
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We propose a Traffic Light approach to backtesting Expected Shortfall which is completely consistent with, and analogous to, the Traffic Light approach to backtesting VaR (Value at Risk) initially proposed by the Basel Committee on Banking Supervision in their 1996 consultative document Basle Committee on Banking Supervision (1996). The approach relies on the generalized coverage test for Expected Shortfall developed in Costanzino and Curran (2015). Full article
Open AccessArticle
Company Value with Ruin Constraint in a Discrete Model
Risks 2018, 6(1), 1; doi:10.3390/risks6010001 -
Abstract
Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp (2003)). In this paper
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Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp (2003)). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp (2016)). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry. Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in Hipp (2016), Section 2.2.2, also yields optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. Full article
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Open AccessArticle
A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk
Risks 2017, 5(4), 65; doi:10.3390/risks5040065 -
Abstract
In this work, we introduce a general framework for incorporating stochastic recovery into structural models. The framework extends the approach to recovery modeling developed in Cohen and Costanzino (2015, 2017) and provides for a systematic way to include different recovery processes into a
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In this work, we introduce a general framework for incorporating stochastic recovery into structural models. The framework extends the approach to recovery modeling developed in Cohen and Costanzino (2015, 2017) and provides for a systematic way to include different recovery processes into a structural credit model. The key observation is a connection between the partial information gap between firm manager and the market that is captured via a distortion of the probability of default. This last feature is computed by what is essentially a Girsanov transformation and reflects untangling of the recovery process from the default probability. Our framework can be thought of as an extension of Ishizaka and Takaoka (2003) and, in the same spirit of their work, we provide several examples of the framework including bounded recovery and a jump-to-zero model. One of the nice features of our framework is that, given prices from any one-factor structural model, we provide a systematic way to compute corresponding prices with stochastic recovery. The framework also provides a way to analyze correlation between Probability of Default (PD) and Loss Given Default (LGD), and term structure of recovery rates. Full article
Open AccessArticle
Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing
Risks 2017, 5(4), 64; doi:10.3390/risks5040064 -
Abstract
We consider the subject of approximating tail probabilities in the general compound renewal process framework, where severity data are assumed to follow a heavy-tailed law (in that only the first moment is assumed to exist). By using the weak convergence of compound renewal
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We consider the subject of approximating tail probabilities in the general compound renewal process framework, where severity data are assumed to follow a heavy-tailed law (in that only the first moment is assumed to exist). By using the weak convergence of compound renewal processes to α-stable Lévy motion, we derive such weak approximations. Their applicability is then highlighted in the context of an existing, classical, index-linked catastrophe bond pricing model, and in doing so, we specialize these approximations to the case of a compound time-inhomogeneous Poisson process. We emphasize a unique feature of our approximation, in that it only demands finiteness of the first moment of the aggregate loss processes. Finally, a numerical illustration is presented. The behavior of our approximations is compared to both Monte Carlo simulations and first-order single risk loss process approximations and compares favorably. Full article
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Open AccessEditorial
Special Issue “Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance”
Risks 2017, 5(4), 63; doi:10.3390/risks5040063 -
Abstract
The aim of the Special Issue is to address some of the main challenges individuals and companies face in managing financial and actuarial risks, when dealing with their investment/retirement or business-related decisions [...] Full article
Open AccessFeature PaperArticle
An Analysis and Implementation of the Hidden Markov Model to Technology Stock Prediction
Risks 2017, 5(4), 62; doi:10.3390/risks5040062 -
Abstract
Future stock prices depend on many internal and external factors that are not easy to evaluate. In this paper, we use the Hidden Markov Model, (HMM), to predict a daily stock price of three active trading stocks: Apple, Google, and Facebook, based on
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Future stock prices depend on many internal and external factors that are not easy to evaluate. In this paper, we use the Hidden Markov Model, (HMM), to predict a daily stock price of three active trading stocks: Apple, Google, and Facebook, based on their historical data. We first use the Akaike information criterion (AIC) and Bayesian information criterion (BIC) to choose the numbers of states from HMM. We then use the models to predict close prices of these three stocks using both single observation data and multiple observation data. Finally, we use the predictions as signals for trading these stocks. The criteria tests’ results showed that HMM with two states worked the best among two, three and four states for the three stocks. Our results also demonstrate that the HMM outperformed the naïve method in forecasting stock prices. The results also showed that active traders using HMM got a higher return than using the naïve forecast for Facebook and Google stocks. The stock price prediction method has a significant impact on stock trading and derivative hedging. Full article
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Open AccessFeature PaperArticle
Bounded Brownian Motion
Risks 2017, 5(4), 61; doi:10.3390/risks5040061 -
Abstract
Diffusions are widely used in finance due to their tractability. Driftless diffusions are needed to describe ratios of asset prices under a martingale measure. We provide a simple example of a tractable driftless diffusion which also has a bounded state space. Full article
Open AccessFeature PaperArticle
Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains
Risks 2017, 5(4), 58; doi:10.3390/risks5040058 -
Abstract
In this paper, we investigate the impact of the accident reporting strategy of drivers, within a Bonus-Malus system. We exhibit the induced modification of the corresponding class level transition matrix and derive the optimal reporting strategy for rational drivers. The hunger for bonuses
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In this paper, we investigate the impact of the accident reporting strategy of drivers, within a Bonus-Malus system. We exhibit the induced modification of the corresponding class level transition matrix and derive the optimal reporting strategy for rational drivers. The hunger for bonuses induces optimal thresholds under which, drivers do not claim their losses. Mathematical properties of the induced level class process are studied. A convergent numerical algorithm is provided for computing such thresholds and realistic numerical applications are discussed. Full article
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Open AccessArticle
A Review and Some Complements on Quantile Risk Measures and Their Domain
Risks 2017, 5(4), 59; doi:10.3390/risks5040059 -
Abstract
In the present paper, we study quantile risk measures and their domain. Our starting point is that, for a probability measure Q on the open unit interval and a wide class LQ of random variables, we define the quantile risk measure ϱ
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In the present paper, we study quantile risk measures and their domain. Our starting point is that, for a probability measure Q on the open unit interval and a wide class LQ of random variables, we define the quantile risk measure ϱQ as the map that integrates the quantile function of a random variable in LQ with respect to Q. The definition of LQ ensures that ϱQ cannot attain the value + and cannot be extended beyond LQ without losing this property. The notion of a quantile risk measure is a natural generalization of that of a spectral risk measure and provides another view of the distortion risk measures generated by a distribution function on the unit interval. In this general setting, we prove several results on quantile or spectral risk measures and their domain with special consideration of the expected shortfall. We also present a particularly short proof of the subadditivity of expected shortfall. Full article