Explicit Solution to a Certain Non-ELQG Risk-sensitive Stochastic Control Problem

Journal Article · Wed Dec 15 04:00:00 UTC 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-010-9106-9· OSTI ID:21480251

Hata, Hiroaki ^[1]; Sekine, Jun ^[2]

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1. Academia Sinica, Institute of Mathematics (China)
2. Kyoto University, Institute of Economic Research (Japan)

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.

• OSTI ID: 21480251
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 62; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CONTROL THEORY
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
HAZARDS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PROBABILITY
STOCHASTIC PROCESSES