Insurance Mathematics & Economics最新文献

We extend the scope of risk measures for which backtesting methods are available by proposing a new approach for general distortion risk measures. The method relies on a stratification and randomization of risk levels. We illustrate the performance of our backtest in numerical case studies.

Conventional indemnity-based insurance (“conventional insurance”) and index-based insurance (“index insurance”) represent two primary insurance types, each harboring distinct advantages depending on specific circumstances. This paper proposes a novel blended insurance whose payout is a mixture of the two, to achieve enhanced risk mitigation and cost efficiency. We present the product design framework that employs a multi-output neural network (NN) model to determine both the triggering type and the index-based payout level. The proposed framework is then applied to an empirical case involving soybean production coverage in Iowa. Our results demonstrate this blended insurance could generally outperform both conventional and index insurance in enhancing policyholders' utility.

Recently, many studies have adopted the fractional stochastic mortality process in characterising the long-range dependence (LRD) feature of mortality dynamics, while there are still fewer appropriate non-Gaussian fractional models to describe it. We propose a stochastic mortality process driven by a mixture of Brownian motion and modified fractional Poisson process to capture the LRD of mortality rates. The survival probability under this new stochastic mortality model keeps flexibility and consistency with existing affine-form mortality models, which makes the model convenient in evaluating mortality-linked products under the market-consistent method. The formula of survival probability also considers the historical information from survival data, which enables the model to capture historical health records of lives. The LRD feature is reflected by our proposed model in the empirical analysis, which includes the calibration and prediction of survival curves based on recent generation data in Japan and the UK. Finally, the consequent empirical analysis of annuity pricing illustrates the difference of whether this feature is involved in actuarial valuation.

Voluntary terminations of life insurance policies mean customer churns that usually lead to losses. Accurate predictions of voluntary terminations facilitate churn management, the valuation of life insurance policies, and the (asset-liability) management of life insurers. We use real-world data with adequate explanatory variables to evaluate the performance of three machine learning methods relative to the performance of three statistical methods in predicting voluntary terminations. Moreover, we decompose voluntary terminations into surrenders and lapses and find that some factors used to predict surrenders differ from those used to predict lapses. Then, we establish a two-stage model for insurers to take cost-effective actions to reduce the propensities of surrenders and lapses. This model outperforms conventional ones in terms of the resulting NPV (net present value).

This paper examines a stochastic one-period insurance market with incomplete information. The aggregate amount of claims follows a compound Poisson distribution. Insurers are assumed to be exponential utility maximizers, with their degree of risk aversion forming their private information. A premium strategy is defined as a mapping between risk-aversion types and premium rates. The optimal premium strategies are denoted by the pure-strategy Bayesian Nash equilibrium, whose existence and uniqueness are demonstrated under specific conditions on the insurer-specific demand functions. Boundary and monotonicity properties for equilibrium premium strategies are derived.

Extant theoretical work on long-term care (LTC) and its insurance has neglected an important fact: Benefits of LTC insurance as well as the amount of public subsidization of LTC can differ between severe and mild dependency. The objective of this paper is to revisit the study of optimal purchase of LTC insurance and its crowding out by public subsidies dissociating coverage for the risk of dependency in nursing home and of dependency at home. This study examines three prevalent models of LTC insurance indemnities commonly encountered in various LTC insurance markets. It also studies the presence of potential intergenerational moral hazard and shows how it drives the crowding out or crowding in of LTC insurance by public subsidization according to the insurance models and risk aversion behaviours.

We build a life insurance model in the tradition of Richard (1975) and Pliska and Ye (2007). Two agents purchase life insurance by continuously paying two premiums. At the random time of death of an agent, the life insurance payment is added to the household wealth to be used by the other agent. We allow for the agents to discount future utilities at different rates, which implies that the household has inconsistent time preferences. To solve the model, we employ the equilibrium of Ekeland and Lazrak (2010), and we derive a new dynamic programming equation which is designed to find this equilibrium for our model. The most important contribution of the paper is to combine the issue of inconsistent time preferences with the presence of several agents. We also investigate the sensitivity of the behaviors of the agents to the parameters of the model by using numeric analysis. We find, among other things, that while the purchase of life insurance of one agent increases in her own discount rate, it decreases in the discount rate of the other agent.

This paper studies the optimal consumption, investment, health insurance and life insurance strategy for a wage earner with smooth ambiguity, habit formation and biometric risks. The individual can invest in the financial market composed of a risk-free asset and a risky asset whose unknown market price results in ambiguity. The habit formation depends on historical consumption and satisfies an ordinary differential equation. Moreover, the biometric risks, which consist of health shock risk and mortality risk, can impact the individual's income and health state. The individual can purchase health insurance and life insurance to respectively deal with health shock risk and mortality risk, and aims at maximizing the total expected utility of consumption, legacy and terminal wealth. Using the dynamic programming technique, we derive the corresponding Hamilton-Jacobi-Bellman equation in the states of health and critical illness respectively, prove the verification theorem and obtain closed-form solutions for the optimal strategies. Finally, numerical experiments are carried out to illustrate the impact of risk aversion, ambiguity aversion, health shock and habit formation on the optimal strategy. The results reveal that the wage earner with different utility functions and different health states will show different behaviors in consumption, investment and insurance purchase.

We provide new results about the comparative static effects of income risk and interest rate risk on optimal risk-reduction and saving decisions. We combine arguments from the risk apportionment literature with monotone comparative statics. Risk reduction and saving are Edgeworth-Pareto substitutes for (mixed) risk averters and Edgeworth-Pareto complements for (mixed) risk lovers. For changes in income risk, risk reduction and saving are Nth-degree risk complements for risk lovers. For changes in interest rate risk, risk reduction and saving are Nth-degree risk substitutes for risk averters. The individual's risk attitude and the source of risk thus co-determine the effects of risk changes on optimal. We also discuss several extensions including multiple loss states, higher-order risk reduction, stochastic dominance, non-separable utility, and inflation risk.

We propose a ‘buy, hold, sell’ (BHS) deterministic lifecycle strategy that involves buying and holding assets until they are sold to generate income. Savings are invested entirely into a risky portfolio until a pre-specified ‘switch age’ and then entirely into a risk-free portfolio after the switch age, followed by withdrawing during the payout phase from both portfolios based on annuitization factors that vary with age. We also allow for access to mortality credits through an insurance market. We analytically derive the dynamics of the investment strategy and show that the strategy is optimal for a range of investors with HARA risk preferences. We demonstrate numerically that the BHS strategy delivers limited loss of utility versus an optimal solution for investors with CRRA preferences and low-moderate levels of risk aversion while significantly outperforming deterministic strategies commonly seen in practice. The BHS strategy offers an attractive alternative for practical applications as it is straightforward to apply while avoiding the need for dynamic optimization and portfolio rebalancing.