Insurance Mathematics & Economics最新文献

This paper exploits the influence of the policyholder's health status on the optimal time at which the policyholder decides to stop paying health-dependent premiums and starts withdrawing health-dependent benefits from a variable annuity (VA) contract accompanied by a guaranteed lifelong withdrawal benefit (GLWB). A mixed continuous-discrete time model is developed to find the optimal time for withdrawal regime initiation. The model determines the investment and disinvestment triggers according to the market conditions for both dynamic and static cases. In the static case, the optimal time is computed at the policy's inception time. In contrast, in the dynamic case, the optimal initiation time is achieved by recursive calculation of the exercise frontier of a real deferral option. Another finding is the sensitivity analysis of the contract concerning the insurance fee and the age of the policyholder.

We propose a general framework for studying optimal issue of CAT bonds in the presence of uncertainty on the parameters. In particular, the intensity of arrival of natural disasters is inhomogeneous and may depend on unknown parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the classical Bayes rule. Taking these progressive prior-adjustments into account, we characterize the optimal policy through a quasi-variational parabolic equation, which can be solved numerically. We provide examples of application in the context of hurricanes in Florida.

In this paper, we study the worst-case distortion risk measure for a given risk when information about distortion functions is partially available. We obtain the explicit forms of the worst-case distortion functions for several different sets of plausible distortion functions. When there is no concavity constraint on distortion functions, the worst-case distortion function is independent of the risk to be measured and the corresponding worst-case distortion risk measure is the weighted average of the VaR's of the risk for all decision makers. When the concavity constraint is imposed on distortion functions and the set of concave distortion functions is defined by the riskiness of one single risk, the explicit form of the worst-case distortion function is obtained, which depends the risk to be measured. When the set of concave distortion functions is defined by the riskiness of multiple risks, we reduce the infinite-dimensional optimization problem to a finite-dimensional optimization problem which can be solved numerically. Finally, we apply the worst-case risk measure to optimal decision making in reinsurance.

We consider an insurance market consisting of multiple competitive insurers with a mean field interaction via their terminal wealth under the exponential utility with relative performance. It is assumed that each insurer regulates her risk by controlling the number of policies. We respectively establish the constant Nash equilibrium (independent of time) on the investment and risk control strategy for the finite n-insurer game and the constant mean field equilibrium for the corresponding mean field game (MFG) problem (when the number of insurers tends to infinity). Furthermore, we examine the convergence relationship between the constant Nash equilibrium of finite n-insurer game and the mean field equilibrium of the corresponding MFG problem. Our numerical analysis reveals that, for a highly competitive insurance market consisting of many insurers, every insurer will invest more in risky assets and increase the total number of outstanding liabilities to maximize her exponential utility with relative performance.

Tail Mean-Variance (TMV) has emerged from the actuarial community as a criterion for risk management and portfolio selection, with a focus on extreme losses. The existing literature on portfolio optimization under the TMV criterion relies on the plug-in approach that substitutes the unknown mean vector and covariance matrix of asset returns in the optimal portfolio weights with their sample counterparts. However, the plug-in method inevitably introduces estimation risk and usually leads to poor out-of-sample portfolio performance. To address this issue, we propose a combination of the plug-in and 1/N rules and optimize its expected out-of-sample performance. Our study is based on the Mean-Variance-Standard-deviation (MVS) performance measure, which encompasses the TMV, classical Mean-Variance, and Mean-Standard-Deviation (MStD) as special cases. The MStD criterion is particularly relevant to mean-risk portfolio selection when risk is measured by quantile-based risk measures. Our proposed combined portfolio consistently outperforms both the plug-in MVS and 1/N portfolios in simulated and real-world datasets.

We examine Pareto-efficient contracts and Stackelberg Equilibria (SE) in a sequential-move insurance market in which a central monopolistic insurer on the supply side contracts with multiple policyholders on the demand side. We obtain a representation of Pareto-efficient contracts when the monopolistic insurer's preferences are represented by a coherent risk measure. We then obtain a representation of SE in this market, and we show that the contracts induced by an SE are Pareto-efficient. However, we note that SE do not induce a welfare gain to the policyholders in this case, echoing the conclusions of recent work in the literature. The social welfare implications of this finding are examined through an application to the flood insurance market of the United States of America, in which we find that the central insurer has a strong incentive to raise premia to the detriment of the policyholders. Accordingly, we argue that monopolistic insurance markets are problematic, and must be appropriately addressed by external regulation.

We propose a novel approach in the assessment of a random risk variable X by introducing magnitude-propensity risk measures $(m_X,p_X)$. This bivariate measure intends to account for the dual aspect of risk, where the magnitudes x of X tell how high are the losses incurred, whereas the probabilities $P(X=x)$ reveal how often one has to expect to suffer such losses. The basic idea is to simultaneously quantify both the severity $m_X$ and the propensity $p_X$ of the real-valued risk X. This is to be contrasted with traditional univariate risk measures, like VaR or CVaR, which typically conflate both effects. In its simplest form, $(m_X,p_X)$ is obtained by mass transportation in Wasserstein metric of the law of X to a two-points $\{0,m_X\}$ discrete distribution with mass $p_X$ at $m_X$. The approach can also be formulated as a constrained optimal quantization problem. This allows for an informative comparison of risks on both the magnitude and propensity scales. Several examples illustrate the usefulness of the proposed approach. Some variants, extensions and applications are also considered.

Mortality risk sharing pools including group self-annuitisation, pooled annuity funds and tontines have been developed as an effective solution for managing longevity risk. Although they have been widely studied in the literature, these mortality risk sharing pools do not consider individual health or functional disability status nor the need for long-term care (LTC) insurance at older ages. We extend these pools to include functional disability and chronic illness and present a matrix-based methodology for pooling mortality risk across heterogeneous individuals classified by functional disability states and chronic illness statuses. We demonstrate how individuals with different health risks can more equitably share mortality risk in a pooled annuity design. A multi-state pool is formed by pooling annuitants considering both longevity and LTC risks and determining the actuarially fair benefits based on individuals' health states. Our methodology provides a general structure for a pooled annuity product that can be applied for general multi-state models. We present an extensive analysis with numerical examples using the US Health and Retirement Study (HRS) data. Our results compare expected annuity benefits for individuals in poor health to those in good health, show the effects of incorporating systematic trends and uncertainty, assess how the valuation of the expected annuity payments interacts with the assumptions used for the multi-state model and assess the impact of pool size.

Quantiles of the mortality rates are relevant in life insurance to control longevity risk properly. Recently, Santolino (2020) adapts the framework of the popular Lee-Carter model to compute the conditional quantiles of the mortality rates. The parameters of the quantile Lee-Carter model are fitted on the mortality data of the population of interest, ignoring the information related to the others. In this paper, we show that more robust parameter estimates can be obtained exploiting the mortality experiences of multiple populations. A neural network is employed to calibrate individual quantile Lee-Carter models jointly using all the available mortality data. In this setting, some common network parameters are used to learn the age and period effects of multiple quantile LC models. Numerical experiments performed on all the countries of the Human Mortality Database validate our approach. The predictions obtained considering the median level appear more accurate than those obtained with the mean models; moreover, those at the tail quantile levels capture the future mortality evolution of the populations well.

We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is flexibly characterized by a random effect which follows a discrete probability distribution drawn from a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model for the joint distribution of the time to events. An efficient MCMC sampler is developed for inference. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance portfolio previously analysed by Milhaud and Dutang (2018). The approach yields an improved predictive performance of the surrending rates.