Explicit Solution to a Certain Non-ELQG Risk-sensitive Stochastic Control Problem
Explicit Solution to a Certain Non-ELQG Risk-sensitive Stochastic Control Problem
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DOI：
10.1007/s00245-010-9106-9
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发表时间：
2010-06
影响因子：
1.8
通讯作者：
H. Hata;J. Sekine
中科院分区：
文献类型：
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作者：
H. Hata;J. Sekine
研究了具有有限/无限时域的风险敏感随机控制问题，其中一维受控过程由线性规划定义，漂移中带有线性控制项。在准则函数中，通过使用Riccati微分方程的解来引入非线性/二次项，因此，问题一般不是ELQG（指数线性二次高斯）。对于该问题，以显式形式计算最优值和控制，并以具体形式给出容许的风险敏感参数集。作为应用，本文研究了两类大偏差控制问题，最大化上行大偏差概率和最小化下行大偏差概率。
A risk-sensitive stochastic control problem with finite/infinite horizon is studied with a 1-dimensional controlled process defined by a linear SDE with a linear control-term in the drift. In the criterion function, a non-linear/quadratic term is introduced by using the solution to a Riccati differential equation, and hence, the problem is not ELQG (Exponential Linear Quadratic Gaussian) in general. For the problem, optimal value and control are calculated in explicit forms and the set of admissible risk-sensitive parameters is given in a concrete form. As applications, two types of large deviations control problems, i.e., maximizing an upside large deviations probability and minimizing a downside large deviations probability, are mentioned.