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.     

Pricing Annuity Guarantees Under a Regime-Switching Model

Abstract

We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees.     

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.     

Patterns of Aging-Related Changes on the Way to 100

Abstract

The objective of this paper is to investigate dynamic properties of age trajectories of physiological indices and their effects on mortality risk and longevity using longitudinal data on more than 5,000 individuals collected in biennial examinations of the Framingham Heart Study (FHS) original cohort during about 50 subsequent years of follow-up. We first performed empirical analyses of the FHS longitudinal data. We evaluated average age trajectories of indices describing physiological states for different groups of individuals and established their connections with mortality risk. These indices include body mass index, diastolic blood pressure, pulse pressure, pulse rate, level of blood glucose, hematocrit, and serum cholesterol. To be able to investigate dynamic mechanisms responsible for changes in the aging human organisms using available longitudinal data, we further developed a stochastic process model of human mortality and aging, by including in it the notions of “physiological norms,” “allostatic adaptation and allostatic load,” “stress resistance,” and other characteristics associated with the internal process of aging and the effects of external disturbances. In this model, the persistent deviation of physiological indices from their normal values contributes to an increase in morbidity and mortality risks. We used the stochastic process model in the statistical analyses of longitudinal FHS data. We found that different indices have different average age patterns and different dynamic properties. We also found that age trajectories of long-lived individuals differ from those of the shorter-lived members of the FHS original cohort for both sexes. Using methods of statistical modeling, we evaluated “normal” age trajectories of physiological indices and the dynamic effects of allostatic adaptation. The model allows for evaluating average patterns of aging-related decline in stress resistance. This effect is captured by the narrowing of the U-shaped mortality risk (considered a function of physiological state) with age. We showed that individual indices and their rates of change with age, as well as other measures of individual variability, manifested during the life course are important contributors to mortality risks. The advantages and limitations of the approach are discussed.     

Majority and Minority Ownership of Publicly-Traded Firms: A Test of the Value of Control Using Market Multiples

Publicly-traded companies that are controlled by other publicly-traded companies provide a unique setting in which to test whether the market values of majority and minority ownership interests are proportionate to their ownership percentages. Test results indicate that the value of subsidiary net assets and net income are greater to majority shareholders than to minority shareholders. However, comparison of asset and income valuation with a sample of diffusely-held firms indicates that this valuation asymmetry is not due to a wealth transfer from the minority to the majority owners but to a discounting of the portion of the subsidiary owned by the minority shareholders.