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1.
跳扩散盈余过程的最优投资和最优再保险   总被引:1,自引:1,他引:0  
梁志彬 《数学学报》2008,51(6):1195-120
站在保险人的立场上,研究了跳扩散盈余过程的最优投资和最优再保险问题.在方差保费原理下,以盈余终值的期望指数效用达到最大作为最优准则,给出了最优策略和值函数的近似表达式.同时也证明了投资总比不投资好的结论.最后,通过一些数例和图表来进一步说明所获得的结论.  相似文献   

2.
In this paper, we consider the optimal proportional reinsurance strategy in a risk model with multiple dependent classes of insurance business, which extends the work of Liang and Yuen (2014) to the case with the reinsurance premium calculated under the expected value principle and to the model with two or more classes of dependent risks. Under the criterion of maximizing the expected exponential utility, closed-form expressions for the optimal strategies and value function are derived not only for the compound Poisson risk model but also for the diffusion approximation risk model. In particular, we find that the optimal reinsurance strategies under the expected value premium principle are very different from those under the variance premium principle in the diffusion risk model. The former depends not only on the safety loading, time and interest rate, but also on the claim size distributions and the counting processes, while the latter depends only on the safety loading, time and interest rate. Finally, numerical examples are presented to show the impact of model parameters on the optimal strategies.  相似文献   

3.
In this paper, under the criterion of maximizing the expected exponential utility of terminal wealth, we study the optimal proportional reinsurance and investment policy for an insurer with the compound Poisson claim process. We model the price process of the risky asset to the constant elasticity of variance (for short, CEV) model, and consider net profit condition and variance reinsurance premium principle in our work. Using stochastic control theory, we derive explicit expressions for the optimal policy and value function. And some numerical examples are given.  相似文献   

4.
This paper considers the optimal investment and premium control problem in a diffusion approximation to a non-homogeneous compound Poisson process. In the nonlinear diffusion model, it is assumed that there is an unspecified monotone function describing the relationship between the safety loading of premium and the time-varying claim arrival rate. Hence, in addition to the investment control, the premium rate can be served as a control variable in the optimization problem. Specifically, the problem is investigated in two cases: (i) maximizing the expected utility of terminal wealth, and (ii) minimizing the probability of ruin respectively. In both cases, some properties of the value functions are derived, and closed-form expressions for the optimal policies and the value functions are obtained. The results show that the optimal investment policy and the optimal premium control policy are dependent on each other. Most interestingly, as an example, we show that the nonlinear diffusion model reduces to a diffusion model with a quadratic drift coefficient when the function associated with the premium rate and the claim arrival rate takes a special form. This example shows that the model of study represents a class of nonlinear stochastic control risk model.  相似文献   

5.
This paper is concerned with the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk. We deal with the problem by exploring the relationship between maximizing the adjustment coefficient and maximizing the expected utility of wealth for the exponential utility function, both with respect to the retained risk of the insurer.Assuming that the premium calculation principle is a convex functional and that some other quite general conditions are fulfilled, we prove the existence and uniqueness of solutions and provide a necessary optimal condition. These results are used to find the optimal reinsurance policy when the reinsurance premium calculation principle is the expected value principle or the reinsurance loading is an increasing function of the variance. In the expected value case the optimal form of reinsurance is a stop-loss contract. In the other cases, it is described by a nonlinear function.  相似文献   

6.
This paper considers a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who is uncertain about the model parameters. We assume that the surplus of the insurance company can be allocated to the financial market consisting of one risk-free asset and one risky asset whose price process satisfies square root factor process. Under the objective of maximizing the expected utility of the terminal surplus, by adopting the technique of stochastic control, closed-form expressions of the robust optimal strategy and the corresponding value function are derived. The verification theorem is also provided. Finally, by presenting some numerical examples, the impact of some parameters on the optimal strategy is illustrated and some economic explanations are also given. We find that the robust optimal reinsurance strategies under the generalized mean–variance premium are very different from that under the variance premium principle. In addition, ignoring model uncertainty risk will lead to significant utility loss for the AAI.  相似文献   

7.
In this paper, we consider the optimal portfolio selection problem in continuous-time settings where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has the structure of the HARA family and the market states change according to a Markov process. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the random asset returns as well as the utility function. We analyzed Black–Scholes type continuous-time models where the market parameters are driven by Markov processes. The Markov process that affects the state of the market is independent of the underlying Brownian motion that drives the stock prices. The problem of maximizing the expected utility of the terminal wealth is investigated and solved by stochastic optimal control methods for exponential, logarithmic and power utility functions. We found explicit solutions for optimal policy and the associated value functions. We also constructed the optimal wealth process explicitly and discussed some of its properties. In particular, it is shown that the optimal policy provides linear frontiers.  相似文献   

8.
结合保险人和再保险人的共同利益,研究了具有两类相依险种风险模型下的最优再保险问题.假定再保险公司采用方差保费原理收取保费,利用复合Poisson模型和扩散逼近模型两种方式去刻画保险公司和再保险公司的资本盈余过程,在期望效用最大准则下,证明了最优再保险策略的存在性和唯一性,通过求解Hamilton-Jacobi-Bellman(HJB)方程,得到了两种模型下相应的最优再保险策略及值函数的明晰解答,并给出了数值算例及分析.  相似文献   

9.
本文研究保险公司在Markov调节下基于时滞及相依风险模型的最优再保险与最优投资问题,其中市场被划分为有限个状态,一些重要的参数随着市场状态的转换而变化.假设保险公司的盈余过程由复合Poisson过程描述,而风险资产的价格过程由几何跳扩散模型刻画,并且假设这两个跳过程是相依的.以最大化终端财富值的均值-方差效用为目标,在博弈论框架下,利用随机控制理论和相应的广义Hamilton-Jacobi-Bellman(HJB)方程,本文得到最优策略和值函数的显式表达,并证明解的存在性和唯一性.最后,通过一些数值实例,验证所得结论的正确性,并探讨一些重要参数对最优策略的影响.  相似文献   

10.
In this paper, we consider the jump‐diffusion risk model with proportional reinsurance and stock price process following the constant elasticity of variance model. Compared with the geometric Brownian motion model, the advantage of the constant elasticity of variance model is that the volatility has correlation with the risky asset price, and thus, it can explain the empirical bias exhibited by the Black and Scholes model, such as volatility smile. Here, we study the optimal investment–reinsurance problem of maximizing the expected exponential utility of terminal wealth. By using techniques of stochastic control theory, we are able to derive the explicit expressions for the optimal strategy and value function. Numerical examples are presented to show the impact of model parameters on the optimal strategies. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

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