离散时间单位连结人寿保险合同的局部风险最小对冲策略

单位连结人寿保险合同是保险利益依赖于某特定股票的价格的保险合同 .当保险公司发行这样的保险合同后 ,保险公司将面临金融和被保险人死亡率两类风险 .因此这样的保险合同相当于不完全金融市场上的或有索取权 ,不能利用自我融资交易策略复制出 .本文提出利用不完全市场的局部风险最小对冲方法对冲保险者的风险 .我们在离散时间的框架下给出了局部风险最小对冲策略 .     

连续时间单位连结人寿保险合同的局部风险最小对冲策略

单位连结人寿保险合同是保险利益依赖于某特定股票的价格的保险合同。本提出利用不完全市场的局部风险最小对冲方法对冲保险的风险。我们在连续时间的框架下给出了局部风险最小对冲策略。     

权益连结生存人寿保险合同的局部风险最小对冲策略

权益连结生存人寿保险合同是保险金依赖于某类特定股票的价格的保险合同 .本文主要利用Schweizer[3]引入的不完全市场的局部风险最小理论确定单位关联人寿保险合同的局部风险最小对冲策略 .     

一般支付过程的局部风险最小对冲策略

本文主要研究对冲（套期保值）者的债务由一般的支付流描述时的局部风险最小对冲策略决定问题。我们在风险资产的价格过程在原概率测度下为半鞅的假设下，证明了局部风险最小对冲策略的存在性和唯一性。我们的结果包含了以前的局部风险最小对冲策略。在鞅的情形中，我们的局部风险最小对冲策略简化为Moller[5]的风险最小对冲策略。     

伪造风险损失欺诈博弈与最优保险合同设计

运用不完全信息动态博弈和机制设计的有关理论，建立了伪造风险损失欺诈博弈模型，研究了伪造风险损失欺诈博弈问题的纳什均衡及其保险双方的最优博弈策略。在此基础上，得出了使保险人的期望利润为零的保险定价公式，讨论了基于保险双方最优博弈策略的最优保险合同形式，证明了基于保险双方最优博弈策略的保险合同是部分保险。     

最小叉熵优化模型在保险定价中的应用研究

为了更加合理解决保险定价问题，本文引入金融风险中性定价思想，提出新的保险定价方法。在不完全的保险市场，利用信息论领域中推测概率分布的最小叉熵优化模型，对经验损失分布进行调整，得到保险风险中性最小叉熵密度，进而确定新的保费。结果表明最小叉熵密度使高风险的比例增大，这体现了风险中性的本质。该保险定价方法的形式是确定的，且所建的最小叉熵优化模型具有灵活、简便的特性。     

保险赔付中的最优对冲策略

本文对带有付费过程$A_t$的保险公司在金融市场$(S_t,Q_t,B_t)$上通过购买股票$S_t$、兑换外币$Q_t$以及购买无风险资产$B_t$的投资过程而采取的最优投资策略, 使保险公司所面临的风险最小进行探讨. 利用Galtchouk-Kunita-Watanabe分解定理将风险表达式重新表达, 从而找到保险公司所能采取的风险最小的最优对冲策略. 文中举出一个具有现实性意义的例子将文章的重要结论加以应用, 使本文更具有应用价值.     

VaR测度下的风险对冲策略研究

本文分别在正态分布和任意分布设定下讨论最小在险价值(VaR)的风险对冲问题。在正态分布设定下,本文深入讨论最小方差对冲比率和最小VaR对冲比率的性质,并得出最小VaR对冲策略下组合收益率的均值和方差大于最小方差策略下组合收益率的均值和方差。在任意分布设定下,本文构建一种新的VaR对冲模型,该模型引入非参数核估计方法对VaR进行估计,然后基于VaR核估计量建立风险对冲问题,实现风险估计与风险对冲同步进行。实证结果非常稳健地表明,不做任何分布假设下的核估计法得到的风险对冲效果优于最小方差对冲策略和正态分布设定下的最小VaR对冲策略。     

保险与再保险及市场对冲稳健均衡策略

假设保险公司的资本盈余过程服从复合Poisson风险跳过程,保险公司通过向再保险公司购买比例再保险来分散保险风险,保险公司和再保险公司均基于方差原则收取保险费率.两个公司都可以投资于金融市场,其中风险资产的价格过程服从几何布朗运动.假设保险公司和再保险公司都是模糊厌恶的且具有指数效用函数,基于保险公司与再保险公司加权终期财富效用最大化目标,利用动态规划原理,得到了两公司的稳健均衡比例再保险和投资组合策略的解析表达式.分析了均衡条件下的风险投资,再保险价格与保险公司自保险比例受不同参变量影响的变化特征.     

基于最小最大鞅测度对保险公司最优投资再保险问题的研究

本文研究既拥有保险公司又拥有再保险公司的大型保险机构的最优管理问题.保险公司可以购买比例再保险,保险公司和再保险公司均可以购买无风险资产和风险资产,大型保险机构的目标是最大化两公司资产加权和的指数效用.通过求解最小最大鞅测度,本文给出了指数效用函数对应的最优策略的精确解.     

Hedging unit‐linked life insurance contracts in a financial market driven by shot‐noise processes

We consider the risk‐minimizing hedging problem for unit‐linked life insurance in a financial market driven by a shot‐noise process. Because the financial market is incomplete, the insurance claims cannot be hedged completely by trading stocks and bonds only, leaving some risk to the insurer. The theory of ((pseudo) locally) risk‐minimization is applied after a change of measure. Then the risk‐minimizing trading strategies and the associated intrinsic risk processes are determined for two types of unit‐linked contracts represented by the pure endowment and the term insurance. Copyright © 2009 John Wiley & Sons, Ltd.     

Pricing and hedging of variable annuities with state-dependent fees

We investigate the problem of pricing and hedging variable annuity contracts for which the fee deducted from the policyholder’s account depends on the account value. It is believed that state-dependent fees are beneficial to policyholders and insurers since they reduce policyholders’ incentives to lapse the policies and match the costs incurred by policyholders with the pay-offs received from embedded guarantees. We consider an incomplete financial market which consists of two risky assets modelled with a two-dimensional Lévy process. One of the assets is a security which can be traded by the insurer, and the second asset is a security which is the underlying fund for the variable annuity contract. In our model we derive an equation from which the fee for the guaranteed benefit can be calculated and we characterize a strategy which allows the insurer to hedge the benefit. To solve the pricing and hedging problem in an incomplete financial market we apply a quadratic objective.     

标准差准则下的最优再保险

本文关注的是在标准差准则下如何进行再保险, 使得保险公司和再保险公司的风险波动达到最小. 在容许合约类范围内得到了建立最优再保险合约的充分条件. 如果再保险公司的风险小于一个给定阈值, 我们找到了使保险公司的风险最小的最优再保险合约. 在这里, 保险公司可以采取三种最一般且有效的风险措施.     

免赔额保险公平定价的期权博弈分析

传统保险定价实质上是供给方定价,忽视了保险契约是保险人和投保人双方互动决策的结果.另一方面,保单具有或有权益的性质,这使得近年来金融定价方法得以引入到保险定价中,以反映风险和回报之间的长期均衡关系.借助期权博弈框架引入博弈论和期权定价理论,分析了免赔额保险的公平定价问题,给出了基本模型和扩展模型两种情形下博弈均衡结果,即保单的无套利价值,并发现在扩展模型情形下,投保人的最优投保策略和均衡保险合同均发生变化.     

Reinsurance contract design when the insurer is ambiguity-averse

This paper investigates proportional and excess-loss reinsurance contracts in a continuous-time principal–agent framework, in which the insurer is the agent and the reinsurer is the principal. Insurance claims follow the classic Cramér–Lundberg process. The insurer believes that the claim intensity is uncertain and he chooses robust risk retention levels to maximize the penalty-dependent multiple-priors utility. The reinsurer designs reinsurance contracts subject to the insurer’s incentive compatibility constraints. The analytical expressions of the two robust reinsurance contracts are derived. Our results show that the robust reinsurance demand and price are greater than their respective standard values without model ambiguity, and increase as the insurer’s ambiguity aversion increases. Moreover, the reinsurer specifies a decreasing reinsurance price to induce increasing demand over time. Specifically, the price of excess-loss reinsurance is higher, relative to that of proportional reinsurance. Further, only if the insurer’s risk aversion is high or the reinsurer’s risk aversion is low, the insurer prefers the excess-loss reinsurance contract.     

Reducing risk by merging counter-monotonic risks

In this article, we show that some important implications concerning comonotonic couples and corresponding convex order relations for their sums cannot be translated to counter-monotonicity in general. In a financial context, it amounts to saying that merging counter-monotonic positions does not necessarily reduce the overall level of risk. We propose a simple necessary and sufficient condition for such a merge to be effective. Natural interpretations and various characterizations of this condition are given. As applications, we develop cancelation laws for convex order and identify desirable structural properties of insurance indemnities that make an insurance contract universally marketable, in the sense that it is appealing to both the policyholder and the insurer.     

Pareto-optimal reinsurance arrangements under general model settings

In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. For the purpose of practice, we use numerical examples to show how to determine the mutually acceptable Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer’s aim and the reinsurer’s goal can be met under the mutually acceptable Pareto-optimal reinsurance contracts.     

Equilibrium relationships between insurance and self-protection activity

When an insured understakes some costly self-protection activity that reduces the probability of loss, a competitive insurer will increase the insurance coverage, given a fixed premium per dollar of coverage, to reflect the lower insurance risk.However, an imperfectly informed insurer cannot correctly adjust the coverage; while he can observe the self-protection activity of the insured, the insurer cannot determine the cost to the insured of such activity, nor can the insurer determine the reduction in the loss probability of the insured due to the self-protection activity.This paper demonstrates in an equilibrium model that insurers may be able to use the amount of self-protection activity by an insured as a screen to indicate to the insurer what the loss probability of the insured is, thus allowing the insurer to provide correctly priced insurance to all individuals. The model points out that insurers operating in a market with moral hazard may be able to overcome the adverse incentives of insureds by selectively offering certain insurance contracts contingent upon the insured meeting certain screening requirements; in the model here, self-protection activity is the screen.