Mean-Variance Optimal Reinsurance Arrangements

Reinsurance reduces the risk but it also reduces the potential profit. The aim of the paper is to derive optimal, from the cedent's point of view, reinsurance arrangements balancing the risk measured by variance and expected profits under various mean-variance premium principles of the reinsurer. We find that quota share, excess of loss or combinations of excess of loss with quota share are the optimal rules according to a fixed expected gain of the cedent     

保险公司最优投资及再保险策略

在最大化生存概率和最大化终止时蒯期望效用准则下,通过求解相应的HJB方程,获得了最优投资策略以及最优比例再保险策略的闭式解.这一研究结果易于实时操作,对投资者的决策有直接的指导意义.     

Unbiased premiums for Stop-Loss reinsurance

Abstract

1. Some further consideration will be given here to the problem of unbiased premium estimation for Stop-Loss reinsurance discussed by Vajda [1].     

Optimal Reinsurance Design: A Mean-Variance Approach

In this article, we study an optimal reinsurance model from the perspective of an insurer who has a general mean-variance preference. In order to reduce ex post moral hazard, we assume that both parties in a reinsurance contract are obligated to pay more for a larger realization of loss. We further assume that the reinsurance premium is calculated only based on the mean and variance of the indemnity. This class of premium principles is quite general in the sense that it includes many widely used premium principles such as expected value, mean value, variance, and standard deviation principles. Moreover, to protect the insurer's profit, a lower bound is imposed on its expected return. We show that any admissible reinsurance policy is dominated by a change-loss reinsurance or a dual change-loss reinsurance, depending upon the coefficient of variation of the ceded loss. Further, the change-loss reinsurance is shown to be optimal if the premium loading increases in the actuarial value of the coverage; while it becomes decreasing, the optimal reinsurance policy is in the form of dual change loss. As a result, the quota-share reinsurance is always optimal for any variance-related reinsurance premium principle. Finally, some numerical examples are applied to illustrate the applicability of the theoretical results.     

Optimal Reinsurance Arrangements Under Tail Risk Measures

Regulatory authorities demand insurance companies control their risk exposure by imposing stringent risk management policies. This article investigates the optimal risk management strategy of an insurance company subject to regulatory constraints. We provide optimal reinsurance contracts under different tail risk measures and analyze the impact of regulators' requirements on risk sharing in the reinsurance market. Our results underpin adverse incentives for the insurer when compulsory Value-at-Risk risk management requirements are imposed. But economic effects may vary when regulatory constraints involve other risk measures. Finally, we compare the obtained optimal designs to existing reinsurance contracts and alternative risk transfer mechanisms on the capital market.     

Recursions for Distribution Functions and Stop-Loss Transforms

For any function f on the non-negative integers, we can evaluate the cumulative function o f given by o f ( s )= ~ s x=0 f ( x ) from the values of f by the recursion o f ( s )= o f ( s -1)+ f ( s ). Analogously we can use this procedure t times to evaluate the t -th order cumulative function o t f . As an alternative, in the present paper we shall derive recursions for direct evaluation of o t f when f itself satisfies a certain sort of recursion. We shall also derive recursions for the t -th order tails v t f where v f ( s )= ~ X x=s+1 f ( x ). The recursions can be applied for exact and approximate evaluation of distribution functions and stop-loss transforms of probability distributions. The class of recursions for f includes the classes discussed by Sundt (1992), incorporating the class studied by Panjer's (1981). We discuss in particular convolutions and compound functions.     

最优再保险的两类定价模型

针对停止损失再保险(stop loss reinsurance)，分别运用均值一方差(mean-variance)保费定价原理及效用理论(utility theory)，在再保险人总索赔额的基础之上推导出最优再保险(optimal reinsurance)的保费定价模型。     

Optimal Proportional Reinsurance Policies in a Dynamic Setting

We consider dynamic proportional reinsurance strategies and derive the optimal strategies in a diffusion setup and a classical risk model. Optimal is meant in the sense of minimizing the ruin probability. Two basic examples are discussed.     

An Extension of Arrow's Result on Optimal Reinsurance Contract

We consider the problem of finding reinsurance policies that maximize the expected utility, the stability and the survival probability of the cedent for a fixed reinsurance premium calculated according to the maximal possible claims principle. We show that the limited stop loss and the truncated stop loss are the optimal contracts.     

Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model

Abstract

We consider an optimal reinsurance-investment problem of an insurer whose surplus process follows a jump-diffusion model. In our model the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a “simplified” financial market consisting of a risk-free asset and a risky asset. The dynamics of the risky asset are governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity. The objective of the insurer is to choose an optimal reinsurance-investment strategy so as to maximize the expected exponential utility of terminal wealth. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Explicit forms for the optimal reinsuranceinvestment strategy and the corresponding value function are obtained. Numerical examples are provided to illustrate how the optimal investment-reinsurance policy changes when the model parameters vary.     

Catastrophe Bonds,Reinsurance, and the Optimal Collateralization of Risk Transfer

Catastrophe bonds feature full collateralization of the underlying risk transfer and thus abandon the reinsurance principle of economizing on collateral through diversification of risk transfer. Our analysis demonstrates that this feature places limits on catastrophe bond penetration, even if the structure possesses frictional cost advantages over reinsurance. However, we also show that catastrophe bonds have important uses when buyers and reinsurers cannot contract over the division of assets in the event of insolvency and, more generally, cannot write contracts with a full menu of state‐contingent payments. In this environment, segregation of collateral—in the form of multiple reinsurance companies, as well as catastrophe bond vehicles—can ameliorate inefficiencies due to reinsurance contracting constraints by improving welfare for those exposed to default risk. Numerical simulation illustrates how catastrophe bonds improve efficiency in market niches with correlated risks, or with uneven exposure of buyers to reinsurer default.     

Optimal Reciprocal Reinsurance Treaties Under the Joint Survival Probability and the Joint Profitable Probability

A reinsurance treaty involves two parties, an insurer and a reinsurer. The two parties have conflicting interests. Most existing optimal reinsurance treaties only consider the interest of one party. In this article, we consider the interests of both insurers and reinsurers and study the joint survival and profitable probabilities of insurers and reinsurers. We design the optimal reinsurance contracts that maximize the joint survival probability and the joint profitable probability. We first establish sufficient and necessary conditions for the existence of the optimal reinsurance retentions for the quota‐share reinsurance and the stop‐loss reinsurance under expected value reinsurance premium principle. We then derive sufficient conditions for the existence of the optimal reinsurance treaties in a wide class of reinsurance policies and under a general reinsurance premium principle. These conditions enable one to design optimal reinsurance contracts in different forms and under different premium principles. As applications, we design an optimal reinsurance contract in the form of a quota‐share reinsurance under the variance principle and an optimal reinsurance treaty in the form of a limited stop‐loss reinsurance under the expected value principle.     

A Reexamination of the Corporate Demand for Reinsurance

This study examines the effect of the state of the international reinsurance market on the demand for reinsurance by U.S. insurers using data from the years 1993 through 2000. Both the overall demand for reinsurance and the utilization of foreign reinsurance by U.S. insurers are explored. In addition to supporting the findings of prior literature related to the traditional motives for the corporate demand for insurance, evidence indicates that the state of the U.S. reinsurance industry impacts the amount of reinsurance demanded by U.S. insurers. The study also investigates reasons why U.S. insurers utilize a reinsurance program composed of both U.S. and foreign reinsurers. The results indicate that the decision to utilize some percentage of foreign reinsurance is driven primarily by the financial and operational characteristics of the ceding company such as firm size, group affiliation, and organizational form. However, no support is found for the hypothesis that possible differences between the foreign and U.S. reinsurance markets impact the decision to utilize foreign reinsurance.     

Securitization, Insurance, and Reinsurance

This article considers strengths and weaknesses of reinsurance and securitization in managing insurable risks. Traditional reinsurance operates efficiently in managing relatively small, uncorrelated risks and in facilitating efficient information sharing between cedants and reinsurers. However, when the magnitude of potential losses and the correlation of risks increase, the efficiency of the reinsurance model breaks down, and the cost of capital may become uneconomical. At this juncture, securitization has a role to play by passing the risks along to broader capital markets. Securitization also serves as a complement for reinsurance in other ways such as facilitating regulatory arbitrage and collateralizing low-frequency risks.     

基于多目标决策方法的优选模型及其应用研究

在多个备选方案中做选择时,不仅要考虑技术、经济、效益等方面的因素,还要考虑决策者与执行者、理论与现实之间矛盾等方面的影响.针对这一类离散型变量的多目标决策问题,使用ELECTRE II方法,可较好的协调指标间的矛盾,进行方案的优劣排序,为决策者提供合理的建议.     

风险价值法及其在金融风险管理中的应用

探讨了金融工具风险价值测定的有关问题，包括风险价值的含义、金融工具风险价值测定的数理基础和具体方法等，并论述了风险价值在风险管理中的应用。     

Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion

The quest for optimal reinsurance design has remained an interesting problem among insurers, reinsurers, and academicians. An appropriate use of reinsurance could reduce the underwriting risk of an insurer and thereby enhance its value. This paper complements the existing research on optimal reinsurance by proposing another model for the determination of the optimal reinsurance design. The problem is formulated as a constrained optimization problem with the objective of minimizing the value-at-risk of the net risk of the insurer while subjecting to a profitability constraint. The proposed optimal reinsurance model, therefore, has the advantage of exploiting the classical tradeoff between risk and reward. Under the additional assumptions that the reinsurance premium is determined by the expectation premium principle and the ceded loss function is confined to a class of increasing and convex functions, explicit solutions are derived. Depending on the risk measure's level of confidence, the safety loading for the reinsurance premium, and the expected profit guaranteed for the insurer, we establish conditions for the existence of reinsurance. When it is optimal to cede the insurer's risk, the optimal reinsurance design could be in the form of pure stop-loss reinsurance, quota-share reinsurance, or a combination of stop-loss and quota-share reinsurance.