幂效用函数的无差别定价和套期保值

研究了多维扩散模型幂效用函数的无差别定价和套期保值.通过动态规划方法得到了未定权益的无差别定价和套期保值策略.并证明了无差别定价与风险厌恶指数无关的.  

Vasicek利率模型下带有零息票债券的投资消费模型

应用随机最优控制理论研究 Vasicek利率模型下的投资消费问题，其中假设无风险利率是服从 Vasicek利率模型的随机过程，且与股票价格过程存在一般相关性。假设金融市场由一种无风险资产、一种风险资产和一种零息票债券所构成，投资者的目标是最大化中期消费与终端财富的期望贴现效用。应用变量替换方法得到了幂效用下最优投资消费策略的显示表达式，并分析了最优投资消费策略对市场参数的灵敏度。  

Household consumption, investment and life insurance

This paper develops a continuous-time Markov model for utility optimization of households. The household optimizes expected future utility from consumption by controlling consumption, investments and purchase of life insurance for each person in the household. The optimal controls are investigated in the special case of a two-person household, and we present graphics illustrating how differences between the two persons affect the controls.  

比例保本约束下的最优投资组合选择

本文研究了幂效用函数下带有比例保本约束的最优投资组合选择问题。利用拉格朗日乘子和投资组合复制方法，得到最优财富过程和最优投资组合，推广了带有限制的投资组合的相关结果。  

基于再保险和投资的随机微分博弈

本文研究了具有再保险和投资的随机微分博弈.应用线性-二次控制的理论,在指数效用和幂效用下,求得了最优再保险策略、最优投资策略、最优市场策略和值函数的显示解,推广了文[8]的结果.通过本文的研究,当市场出现最坏的情况时,可以指导保险公司选择恰当的再保险和投资策略使自身所获得的财富最大化.  

幂效用函数的最优投资组合研究

本文对投资组合中较常用的风险厌恶型的幂效用函数进行研究。应用无差异曲线法求解出这种效用函数的最优投资比例,并对本文所得出的结论进行了实例应用分析。  

Portfolio selection in discrete time with transaction costs and power utility function: a perturbation analysis

In this article, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length.  

Power Utility Maximization Problems Under Partial Information and Information Sufficiency in a Brownian Setting

We consider the problem of expected power utility maximization from terminal wealth in diffusion market models under partial information. After obtaining novel neat expressions for the value-process and for the optimal strategy, the issue of information sufficiency is addressed. In particular, necessary and sufficient conditions that guarantee that the partial information optimal strategy is still optimal when having access to all market information, are provided.  

Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utility

In this paper, we assume that an investor can invest his/her wealth in a bond and a stock. In our wealth model, the stochastic interest rate is described by a Cox–Ingersoll–Ross (CIR) model, and the volatility of the stock is proportional to another CIR process. We obtain a closed‐form expression of the optimal policy that maximizes a power utility. Moreover, a verification theorem without the usual Lipschitz assumptions is proved, and the relationships between the optimal policy and various parameters are given. Copyright © 2009 John Wiley & Sons, Ltd.  

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This paper investigate a stochastic differential games for DC (defined contribution plans) pension under Vasicek stochastic interest rate. The finance market as the hypothetical counterpart, the investor as pension the leader of game. Our goal is through the game between pension plan investor and financial market, obtain optimal strategies to maximizes the expected utility of the terminal wealth. Under power utility function, by using stochastic control theory, we obtain closed-form solutions for the value function as well as the strategies. Finally, explain the research results in the economic sense, and though numerical calculation given the influence of some parameters on the optimal strategies