Applied Mathematics & Optimization

, Volume 62, Issue 3, pp 341–380 | Cite as

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

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Abstract

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.

Keywords

Risk-sensitive stochastic control ELQG Riccati differential equation Large deviations control Long-term optimal investment Nonlinear factor Beneš’s filters 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of MathematicsAcademia SinicaTaipeiTaiwan
  2. 2.Institute of Economic ResearchKyoto UniversitySakyo-ku, KyotoJapan

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