Risk-sensitive stochastic control and its singular limit

风险敏感随机控制及其奇异极限

基本信息

批准号：
10440030
负责人：
NAGAI Hideo
金额：
$ 3.33万
依托单位：
OSAKA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

(a) It is important to know the conditions for no breakdown in risk-sensitive stochastic control problems since the value function has not always a finite value. In this research we have obtained the condition as that of the size of risk-sensitive parameter in the case of a finite time horizon and also shown the solvability of the corresponding Bellman equation under the condition. It is applicable for the case that the risk-sensitive parameter is large and has great meaning in application. In the case of infinite time horizon we have shown existence and uniqueness of the corresponding ergodic type Bellman equation under a similar condition by noticing the relationships between the problems and the eigenvalue problems for Schrodinger operator. Besides, we have derived a first order partial differential equation relating to game theoretical approach to nonlinear H_∞ control as its singular limit.(b) We have considered portfolio optimization problem for a factor model as application to m … More athematical finance of risk-sensitive stochastic control and got the results giving the explicit representation to optimal portfolio for the problem in the case of partial information. In the case of infinite time horizon we obtained the condition under which the solution of corresponding ergodic type Bellman equation defines the optimal portfolio and constructed it by the solution. We have also found that the solution does not always give the optimal portfolio without any condition.(c) We have shown existence of the spectral gap of Schrodinger opeartor by using log Sobolev inequality and gave the estimate.(d) We have shown that the large deviation principle holds for additive functional of Brownian motion corresponding to measures in Kato class. As its application we obtained necessary and sufficient condition under which additive functionals converges exponentially fast.(e) We have shown Trotter product formula with respect to L_p and trace norm and their error estimates for the Schrodinger operator with a potential bounded below.(f) We have shown that the sequence of symmetric statistics defined by Weyl transformation on infinite dimensional torus converges to the limit represented by multiple Wiener integral under the probability measures. Less

（a）重要的是要了解风险敏感的随机控制问题的崩溃，因为该功能在这项研究中并不总是一个价值。同样，在这种情况下，相应的Bellman方程很大，在无限时间的情况下，我们已经显示Schrodinger的问题及其特征值的问题时间的情况，我们获得了Solresponding Ergodicn bellman定义最佳投资组合并通过解决方案构造的链接。频谱差距使用lobolev inequlity并给出了timate（d）。指数迅速。较少的。