PDE Approach to Utility Maximization for Market Models with Hidden Markov Factors
PDE Approach to Utility Maximization for Market Models with Hidden Markov Factors
复制标题
DOI：
10.1007/978-3-7643-8458-6_27
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
H. Nagai;W. Runggaldier
中科院分区：
文献类型：
--
作者：
H. Nagai;W. Runggaldier
我们考虑的问题，从终端财富的期望效用最大化的权力效用的风险厌恶型假设的风险资产的动态是由隐藏的“经济因素”，演变为一个有限状态的马尔可夫过程的影响。对于这个部分可观测的随机控制问题，我们确定了一个相应的完整的观察问题，原来是风险敏感型，并为动态规划方法导致一个非线性PDE，通过适当的变换，可以线性。通过概率表示，我们得到了一个独特的粘度解决方案，后者的PDE，诱导一个独特的粘度解决方案，前者。这种概率表示使我们能够获得，一方面，规律性的结果，另一方面，基于蒙特卡罗模拟的计算方法。
We consider the problem of maximizing expected utility from terminal wealth for a power utility of the risk-averse type assuming that the dynamics of the risky assets are affected by hidden “economic factors” that evolve as a finite-state Markov process. For this partially observable stochastic control problem we determine a corresponding complete observation problem that turns out to be of the risk sensitive type and for which the Dynamic programming approach leads to a nonlinear PDE that, via a suitable transformation, can be made linear. By means of a probabilistic representation we obtain a unique viscosity solution to the latter PDE that induces a unique viscosity solution to the former. This probabilistic representation allows us to obtain, on the one hand, regularity results, on the other hand, a computational approach based on Monte Carlo simulation.