Search Results (18)

This paper explores optimal consumption and investment strategies for agents facing mortality risk within a complete financial market. Departing from traditional frameworks, we leverage state-dependent utility theory, discounted by the state–price process, to compare consumption streams and utilize life insurance as a strategic hedging instrument. To model the ability of insurance companies to hedge the mortality risk of consumer pools, we introduce the concept of life insurance completeness, allowing individuals to achieve optimal consumption even in scenarios involving negative wealth. Our model relaxes the stringent integrability conditions commonly imposed in the literature, offering a more economically grounded approach to valuation and hedging. We derive a general solution to the optimization problem using martingale techniques under minimal assumptions, demonstrating that life insurance primarily serves as a mortality risk hedge rather than a bequest motive. This perspective resolves longstanding theoretical and empirical challenges, notably the annuity puzzle, by illustrating that optimal consumption and investment, in the absence of labor income, do not necessitate annuities or other life insurance policies. Our key contributions include (1) extending valuation frameworks to encompass prepaid insurance and less restrictive integrability criteria, (2) establishing life insurance completeness for effective mortality risk hedging, (3) demonstrating the feasibility of optimal consumption under negative wealth and state-dependent preferences, and (4) offering a resolution to the annuity puzzle that aligns with empirical observations. Full article

The paper examines the valuation and hedging of life insurance obligations in the presence of mortality risk using the local risk-minimizing hedging approach. Roughly speaking, it is assumed that the lifetime of policyholders in an insurance portfolio is modeled by a point process whose stochastic intensity is controlled by a diffusion process. The stock price process is assumed to be a regime-switching Lévy process with non-zero regime-switching drift, where the parameters are assumed to depend on the economic states. Using the Föllmer–Schweizer decomposition, the main valuation and hedging results for a conditional payment process are determined. Some specific situations have been considered in which the local risk-minimizing strategies for a stream of liability payments or a unit-linked contract are presented. Full article

Life insurers, whose contractual liabilities include providing minimum guaranteed interest rates to policyholders, are significantly affected by persistently low interest rates. Hence, this study reviews the literature on the prolonged low interest rate environment and its impact on the life insurance industry, incorporating multiple perspectives and practices in different countries. The effect of low interest rates on life insurance products depends on the sensitivity of the interest rate of each product type and the level of minimum interest rate guarantee. In addition, their impacts on the valuation of life insurance companies depend on shifts in the valuation interest rate, which is used to discount the present value of future benefits, as well as the financial and solvency issues faced by insurers. Overall, the literature suggests that insurers need both short- and long-term solutions to respond to a prolonged low interest rate environment. Full article

Actuaries utilize demographic features such as mortality and longevity rates for pricing, valuation, and reserving life insurance and pension contracts. Capturing accurate mortality estimates requires factual mortality assumptions in mortality models. However, the dynamic and uncertain nature of mortality improvements and deteriorations necessitates better approaches in tracking mortality changes, for instance, using the causes of deaths features. This paper aims to determine temporal homogeneous clusters using unsupervised learning, a clustering approach to group causes of death based on (dis)similarity measures to set representative clusters in detection and monitoring death trends. The causes of death dataset were derived from the World Health Organization, Global Health Estimates for males and females, from 2000 to 2019, for Kenya. A hierarchical agglomerative clustering technique was implemented with modified Dynamic Time Warping distance criteria. Between 6 and 14 clusters were optimally achieved for both males and females. Using visualisations, principal clusters were detected. Over time, the causes of death trends of these clusters have demonstrated a correlated association with mortality and longevity rates, rationalizing why insurance and pension offices may include this approach as a preliminary step to undertake mortality and longevity modelling. Full article

This paper addresses the problem of approximating the future value distribution of a large and heterogeneous life insurance portfolio which would play a relevant role, for instance, for solvency capital requirement valuations. Based on a metamodel, we first select a subset of representative policies in the portfolio. Then, by using Monte Carlo simulations, we obtain a rough estimate of the policies’ values at the chosen future date and finally we approximate the distribution of a single policy and of the entire portfolio by means of two different approaches, the ordinary least-squares method and a regression method based on the class of generalized beta distribution of the second kind. Extensive numerical experiments are provided to assess the performance of the proposed models. Full article

The aim of this paper is to provide a stochastic model useful for assessing the capital requirement for demographic risk in a framework coherent with the Solvency II Directive. The model extends to the market consistent context classical methodologies developed in a local accounting framework. The random variable demographic profit, defined in literatue under local accounting principles, is indeed analysed in a Solvency II framework. We provide a unique formulation for different non-participating life insurance contracts and we prove analytically that the valuation of demographic profit can be significantly affected by the financial conditions in the market. Regarding this topic, we implement the Vašíček model to add randomness to risk-free rates. A case study has also been developed considering a portfolio of life insurance contracts. Results prove the effectiveness of the model in highlighting the main drivers of capital requirement evaluation (e.g., the volatility of both mortality rates and risk-free rates), also compared to the local GAAP framework. Full article

The purpose of this paper is to conduct a market-consistent valuation of life insurance participating liabilities sold to a population of partially heterogeneous customers under the joint impact of biometric and financial risk. In particular, the heterogeneity between groups of policyholders stems from their offered minimum interest rate guarantees and contract maturities. We analyse the effects of these features on the company’s insolvency while embracing the insurer’s goal to achieve the same expected return for different cohorts of policyholders. Within our extensive numerical analyses, we determine the fair participation rates and other key figures, and discuss the implications for the stakeholders, taking account of various degrees of conservativeness of the insurer when pricing the contracts. Full article

This study develops a quasi-closed-form solution for the valuation of an American put option and the critical price of the underlying asset. This is an important area of research both because of a large number of transactions for American put options on different underlying assets (stocks, currencies, commodities, etc.) and because this type of evaluation plays a role in determining the value of other financial assets such as mortgages, convertible bonds or life insurance policies. The procedure used is commonly known as the method of lines, which is considered to be a formulation in which time is discrete rather than continuous. To improve the quality of the results obtained, the Richardson extrapolation is applied, which allows the convergence of the outputs to be accelerated to values close to reality. The model developed in this paper derives an explicit formula of the finite-maturity American put option. The results obtained, besides allowing us to quickly determine the option value and the critical price, enable the graphical representation—in two and three dimensions—of the option value as a function of the other components of the model. Full article

The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death over time since insurance companies’ profits and the social security of citizens depend on human survival; therefore, forecasting dynamic life tables could have significant economic and social implications. Quantitative tools such as resampling methods are required to assess the current and future states of mortality behavior. The insurance companies that manage these life tables are attempting to establish models for evaluating the risk of insurance products to develop a proactive approach instead of using traditional reactive schemes. The main objective of this paper is to compare three mortality models to predict dynamic life tables. By using the real data of European countries from the Human Mortality Database, this study has identified the best model in terms of the prediction ability for each sex and each European country. A comparison that uses cobweb graphs leads us to the conclusion that the best model is, in general, the Lee–Carter model. Additionally, we propose a procedure that can be applied to a life table database that allows us to choose the most appropriate model for any geographical area. Full article

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

A variable annuity is a popular life insurance product that comes with financial guarantees. Using Monte Carlo simulation to value a large variable annuity portfolio is extremely time-consuming. Metamodeling approaches have been proposed in the literature to speed up the valuation process. In metamodeling, a metamodel is first fitted to a small number of variable annuity contracts and then used to predict the values of all other contracts. However, metamodels that have been investigated in the literature are sophisticated predictive models. In this paper, we investigate the use of linear regression models with interaction effects for the valuation of large variable annuity portfolios. Our numerical results show that linear regression models with interactions are able to produce accurate predictions and can be useful additions to the toolbox of metamodels that insurance companies can use to speed up the valuation of large VA portfolios. Full article

This paper provides a complete program for the valuation of aggregate non-life insurance liability cash flows based on claims triangle data. The valuation is fully consistent with the principle of valuation by considering the costs associated with a transfer of the liability to a so-called reference undertaking subject to capital requirements throughout the runoff of the liability cash flow. The valuation program includes complete details on parameter estimation, bias correction and conservative estimation of the value of the liability under partial information. The latter is based on a new approach to the estimation of mean squared error of claims reserve prediction. Full article

The replicating portfolio approach is a well-established approach carried out by many life insurance companies within their Solvency II framework for the computation of risk capital. In this note,weelaborateononespecificformulationofareplicatingportfolioproblem. Incontrasttothetwo most popular replication approaches, it does not yield an analytic solution (if, at all, a solution exists andisunique). Further,althoughconvex,theobjectivefunctionseemstobenon-smooth,andhencea numericalsolutionmightthusbemuchmoredemandingthanforthetwomostpopularformulations. Especially for the second reason, this formulation did not (yet) receive much attention in practical applications, in contrast to the other two formulations. In the following, we will demonstrate that the (potential) non-smoothness can be avoided due to an equivalent reformulation as a linear second order cone program (SOCP). This allows for a numerical solution by efficient second order methods like interior point methods or similar. We also show that—under weak assumptions—existence and uniqueness of the optimal solution can be guaranteed. We additionally prove that—under a further similarly weak condition—the fair value of the replicating portfolio equals the fair value of liabilities. Based on these insights, we argue that this unloved stepmother child within the replication problem family indeed represents an equally good formulation for practical purposes. Full article

Traditional participating life insurance contracts with year-to-year (cliquet-style) guarantees have come under pressure in the current situation of low interest rates and volatile capital markets, in particular when priced in a market-consistent valuation framework. In addition, such guarantees lead to rather high capital requirements under risk-based solvency frameworks such as Solvency II or the Swiss Solvency Test (SST). Therefore, insurers in several countries have developed new forms of participating products with alternative (typically weaker and/or lower) guarantees that are less risky for the insurer. In a previous paper, it has been shown that such alternative product designs can lead to higher capital efficiency, i.e., higher and more stable profits and reduced capital requirements. As a result, the financial risk for the insurer is significantly reduced while the main guarantee features perceived and requested by the policyholder are preserved. Based on these findings, this paper now combines the insurer’s and the policyholder’s perspective by analyzing product versions that compensate policyholders for the less valuable guarantees. We particularly identify combinations of asset allocation and profit participation rate for the different product designs that lead to an identical expected profit for the insurer (and identical risk-neutral value for the policyholder), but differ with respect to the insurer’s risk and solvency capital requirements as well as with respect to the real-world return distribution for the policyholder. We show that alternative products can be designed in a way that the insurer’s expected profitability remains unchanged, the insurer’s risk and hence capital requirement is substantially reduced and the policyholder’s expected return is increased. This illustrates that such products might be able to reconcile insurers’ and policyholders’ interests and serve as an alternative to the rather risky cliquet-style products. Full article

Objectives: Chronic Obstructive Pulmonary Disease (COPD) is one of the fastest growing causes of death worldwide. However, few studies, if any, have been conducted that have investigated patient profiles in Asia. This paper analyzes patient willingness to pay (WTP) as a function of patient disease severity, health-related quality of life (HRQL), and smoking behavior in Taiwan. Study Design: A cross-sectional survey was conducted using in-person interviews with COPD patients. A hypothetical scenario was designed and presented to ascertain each subject’s willingness to pay (WTP) for a cure for COPD. Methods: A survey of subjects with COPD was performed in Taiwan. The contingent valuation method (CVM) was employed to measure patient financial burden, which was analyzed along with covariates that included various types of health-related quality of life (HRQL), severity level, and demographic background. Multivariate regression and simulation methods were employed for analysis. Results: A total of 142 subjects were interviewed, with an average annual WTP of approximately $1422 USD (or 42,662.37 NTD, New Taiwan Dollars). The annual WTP for patients 55 years of age or younger, $5709.06, was the highest and equivalent to approximately one-third of Taiwan average annual personal income or quadruple the spending amount of the Taiwan National Bureau of Health Insurance (NBHI) for each COPD patient. Current cigarette smokers were willing to pay a substantially higher amount than former smokers and nonsmokers, which reflects a psychological desire for redemption in COPD patients. Conclusions: The results of this study provide directions for the relevant authorities regarding the alleviation of suffering as a result of COPD. Appropriate health promotion measures, such as measures to reduce tobacco usage, early diagnosis, and active treatment, may be necessary to contain the escalating costs related to COPD and to prevent this epidemic from worsening. Full article