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Maximum Principle for Risk-Sensitive Stochastic Optimal Control Problem and Applications to Finance

Maximum Principle for Risk-Sensitive Stochastic Optimal Control Problem and Applications to Finance This article is concerned with a risk-sensitive stochastic optimal control problem motivated by a kind of optimal portfolio choice problem in the financial market. The maximum principle for this kind of problem is obtained, which is similar in form to its risk-neutral counterpart. But the adjoint equations and maximum condition heavily depend on the risk-sensitive parameter. This result is used to solve a kind of optimal portfolio choice problem and the optimal portfolio choice strategy is obtained. Computational results and figures explicitly illustrate the optimal solution and the sensitivity to the volatility rate parameter. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Stochastic Analysis and Applications Taylor & Francis

Maximum Principle for Risk-Sensitive Stochastic Optimal Control Problem and Applications to Finance

Stochastic Analysis and Applications , Volume 30 (6): 22 – Nov 1, 2012
22 pages

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References (29)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1532-9356
eISSN
0736-2994
DOI
10.1080/07362994.2012.727138
Publisher site
See Article on Publisher Site

Abstract

This article is concerned with a risk-sensitive stochastic optimal control problem motivated by a kind of optimal portfolio choice problem in the financial market. The maximum principle for this kind of problem is obtained, which is similar in form to its risk-neutral counterpart. But the adjoint equations and maximum condition heavily depend on the risk-sensitive parameter. This result is used to solve a kind of optimal portfolio choice problem and the optimal portfolio choice strategy is obtained. Computational results and figures explicitly illustrate the optimal solution and the sensitivity to the volatility rate parameter.

Journal

Stochastic Analysis and ApplicationsTaylor & Francis

Published: Nov 1, 2012

Keywords: Maximum principle; Ornstein-Uhlenbeck model; Riccati equation; Risk-sensitive control; Stochastic optimal control; Primary 93E20, 60H10; Secondary 49K45, 60H30

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