# Remarks on Risk-Sensitive Control Problems

Remarks on Risk-Sensitive Control Problems The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor $\alpha$ goes to zero. If $u_\alpha(\theta,x)$ denotes the optimal cost function, $\theta$ being the risk factor, then it is shown that $\lim_{\alpha\to 0}\alpha u_\alpha(\theta,x)=\xi(\theta)$ where $\xi(\theta)$ is the average on $)0,\theta($ of the optimal cost of the (usual) infinite horizon risk-sensitive control problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Remarks on Risk-Sensitive Control Problems

, Volume 52 (3) – Oct 1, 2005
14 pages

/lp/springer_journal/remarks-on-risk-sensitive-control-problems-VtjFLjirP0
Publisher
Springer-Verlag
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-005-0829-y
Publisher site
See Article on Publisher Site

### Abstract

The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor $\alpha$ goes to zero. If $u_\alpha(\theta,x)$ denotes the optimal cost function, $\theta$ being the risk factor, then it is shown that $\lim_{\alpha\to 0}\alpha u_\alpha(\theta,x)=\xi(\theta)$ where $\xi(\theta)$ is the average on $)0,\theta($ of the optimal cost of the (usual) infinite horizon risk-sensitive control problem.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2005

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