Risk-sensitive Portfolio Optimization with Full and Partial Information
Risk-sensitive Portfolio Optimization with Full and Partial Information
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DOI：
10.2969/aspm/04110257
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
H. Nagai
中科院分区：
文献类型：
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作者：
H. Nagai
本文讨论了风险敏感控制在一般因子模型投资组合优化问题中的应用，该模型被认为是默顿跨期资本资产定价模型（[18]）的一个变体。在该模型中，证券价格的瞬时平均收益率和波动率受经济因素和证券价格的影响。假设经济因素满足随机微分方程，其系数既依赖于证券价格，也依赖于经济因素本身。在马尔可夫环境下的一般不完全市场模型中，我们考虑在有限时间范围内构造风险敏感投资组合优化问题的最优策略。研究了与最优化问题相对应的抛物型Bellman方程。通过对Bellman方程的分析，从方程的解出发，构造了最优策略。我们用部分信息进一步讨论这个问题。我们将利用后向随机偏微分方程得到最优性的一个必要条件。§
We discuss an application of risk-sensitive control to portfolio optimization problems for a general factor model, which is considered a variation of Merton's intertemporal capital asset pricing model ([18]). In the model the instantaneous mean returns as well as volatilities of the security prices are affected by economic factors and the security prices. The economic factors are assumed to satisfy stocahstic differential equations whose coefficients depend on the security prices as well as themselves. In such general incomplete market models under Markovian setting we consider constructing optimal strategies for risk-sensitive portfolio optimization problems on a finite time horizon. We study the Bellman equations of parabolic type corresponding to the optimization problems. Through analysis of the Bellman equations we construct optimal strategies from the solution of the equation. We further discuss the problem with partial information. We shall obtain a necessary condition for optimality using backward stochastic partial differential equations. §