Markov切换具有Knight不确定下最优消费和投资组合研究

发布时间：2018-03-12 19:34

本文选题：Knight不确定　切入点：投资组合　出处：《应用概率统计》2014年04期 　论文类型：期刊论文

【摘要】：本文在模型不确定环境和一般的半鞅市场条件下,考虑来自于消费和终端财富预期效用最大化问题.代理人以一初始资本和一随机禀赋(endowment)进行投资.我们用鞅方法和对偶理论去寻求最优消费和投资组合问题的解,首先,利用对偶原理,给出在适当的假设条件下,该投资组合问题唯一解存在性的证明,同时对该解进行刻画,并推导出原问题和对偶问题的值函数是互为共轭的.此外,我们还考虑了一个跳扩散模型,该跳扩散模型的系数依赖于一个Markov链,且投资者对Markov链状态间的切换的速率是Knight不确定的.在该模型中我们考虑代理人具有对数效用函数时,可用随机控制方法推导其HJB方程,并能给出HJB方程的数值解,进而能推出最优消费和投资策略.
[Abstract]:In this paper, under the uncertain environment of the model and the general semi-martingale market conditions, Considering the problem of maximizing expected utility from consumption and terminal wealth. The agent invests with an initial capital and a random endowment. We use martingale method and duality theory to find the solution of the optimal consumption and portfolio problem. By using the duality principle, the existence of the unique solution of the portfolio problem is proved under proper assumptions. At the same time, the solution is characterized, and the value functions of the original problem and the dual problem are deduced to be conjugate to each other. We also consider a hopping diffusion model whose coefficients depend on a Markov chain and the rate of switching between Markov chains by investors is Knight uncertain. In this model we consider that agents have logarithmic utility functions. The HJB equation can be deduced by the stochastic control method, and the numerical solution of the HJB equation can be given, and the optimal consumption and investment strategy can be deduced.
【作者单位】：安徽工程大学数理学院;
【基金】：国家自然科学基金资助项目(71171003,71271003,11326121) 教育部人文社会科学规划基金项目(12YJA790041) 安徽省自然科学基金资助项目(1408085QA09,1208085MG116) 安徽省高校自然科学基金资助项目(KJ2013B023)资助
【分类号】：F830.59;F224

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