“The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model,” Shuanming Li,October 2008

Abstract

In a first-party recovery scheme for automobile property damage, the first-party insurer compensates not-at-fault vehicular damage. In this scheme, adjusters may not have the incentive to assign liability when the driver is, in fact, at fault for the accident. This is due to adjusters not having to coordinate with a third-party adjuster, and, for insureds that carry collision coverage, the assignment of fault does not appreciably affect the compensation paid out. This in turn reduces the effectiveness of the experience-rating component of the insurance premium. Empirical evidence that supports the presence of incorrect fault assignment is provided. A stochastic model of experience rating analyzing the impact of incorrect fault assignment on driving record classes confirms that low-risk insureds pay more for insurance than if fault was correctly assigned.     

Valuation of Discrete Dynamic Fund Protection Under Lévy Processes

Abstract

This paper investigates the valuation of discrete dynamic fund protection (DFP) under Levy processes. Specifically, the analytical solution of discrete DFP under Lévy processes is obtained in terms of Fourier transforms. The derivation uses Spitzer’s formula and leads to a recursion on computing the characteristic function of the maximum protection-to-fund ratio using the Fourier inversion. DFP can then be valued efficiently and accurately via the fast Fourier transform. The pricing behavior of the discrete DFP is numerically examined using several Levy processes, such as geometric Brownian motion, jump-diffusion models, and variance gamma process. Numerical experiments confirm that the proposed approach produces highly accurate discrete DFP values within 1 second.     

Weighted Pricing Functionals With Applications to Insurance

Abstract

We explore the role of weighted distributions in pricing insurance risks. In particular, we relate the distributions to actuarial and economic premium calculation principles and in this way provide a unifying methodology for constructing new principles and analyzing known ones.     

Backtesting Stochastic Mortality Models

Abstract

This study sets out a backtesting framework applicable to the multiperiod-ahead forecasts from stochastic mortality models and uses it to evaluate the forecasting performance of six different stochastic mortality models applied to English & Welsh male mortality data. The models considered are the following: Lee-Carter’s 1992 one-factor model; a version of Renshaw-Haberman’s 2006 extension of the Lee-Carter model to allow for a cohort effect; the age-period-cohort model, which is a simplified version of Renshaw-Haberman; Cairns, Blake, and Dowd’s 2006 two-factor model; and two generalized versions of the last named with an added cohort effect. For the data set used herein, the results from applying this methodology suggest that the models perform adequately by most backtests and that prediction intervals that incorporate parameter uncertainty are wider than those that do not. We also find little difference between the performances of five of the models, but the remaining model shows considerable forecast instability.     

Household Life Insurance Demand

Abstract

What types of households own life insurance? Who owns term life and who owns whole life insurance? These are questions of great interest to insurers that operate in a highly competitive market. To answer these questions, we jointly examine household demand of two types of insurance, term and whole life, using data from the Survey of Consumer Finances, a probability sample of the U.S. population. We model both the frequency and the severity of demand for insurance, building on the work of Lin and Grace by using explanatory variables that they developed. For the frequency portion, the household decisions about whether to own term and whole life insurance are modeled simultaneously with a bivariate probit regression model. Given ownership of life insurance by a household, the amounts of insurance are analyzed using generalized linear models with a normal copula. The copula permits the bivariate modeling of insurance amounts for households who own both term and whole life insurance, about 20% of our sample. These models allow analysts to predict who owns life insurance and how much they own, an important input to the marketing process.

Moreover, our findings suggest that household demand for term and whole life insurance is jointly determined. After controlling for explanatory variables, there exists a negative relationship for a household’s decision to own both whole and term life insurance (the frequency part) and a positive relationship for the amount of insurance purchased (the severity part). This indicates that the greater the probability of holding one type, the smaller the probability of holding the other type of life insurance. However, higher demand for both types of insurance exists when a household decides to own both. This mixed effect extends prior work that established a negative relationship, suggesting that term life insurance and whole life insurance are substitutes for one another. In contrast, our findings reveal that the ownership decision involves substitution, but, for households owning both types of insurance, amounts are positively related. Therefore, term and whole life insurance are substitutes in the frequency yet complements in the severity.     

Explaining Mortality Dynamics

Abstract

Using data for six OECD countries over the period 1950–2006, this paper studies the impact of macroeconomic fluctuations and cause of death trends on mortality dynamics in the Lee-Carter mortality forecasting model. The key results of this study are the following: (1) Periods can be identified in which the Lee-Carter mortality index k_t correlates significantly with macroeconomic fluctuations. (2) A few causes of death such as diseases of the circulatory system, influenza and pneumonia, and diabetes mellitus account for a large fraction of the variations in the Lee-Carter mortality index k_t . (3) Most cause-specific mortality rates show pronounced trends over the last few decades. These trends change the composition of deaths and alter how total mortality reacts to external factors such as macroeconomic fluctuations.     

Fair Valuation of Equity-Linked Policies under Insurer Default Risk

Abstract

We consider the problem of computing the fair value of equity-linked policies with an interestrate guarantee when the insurer is subject to credit risk. The framework is developed based on modern financial theory using the no-arbitrage principle. In this context, an equity-linked policy is considered as a vulnerable contingent claim that expires before maturity if the firm asset value reaches a prespecified default threshold depending on the firm’s liabilities. We derive a closedform formula in a continuous-time environment to compute the fair value of the contract. We also develop a discrete-time model that allows us to address fair evaluation when the policy embeds a surrender option.