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A note on long-term optimal portfolios under drawdown constraints

Part of: Stochastic systems and control Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  01 July 2016

Jun Sekine
Jun Sekine*
Affiliation:
Kyoto University
*
∗ Postal address: Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501, Japan. Email address: [email protected]
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Abstract

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The maximization of the long-term growth rate of expected utility is considered under drawdown constraints. In a general situation, the value and the optimal strategy of the problem are related to those of another ‘standard’ risk-sensitive-type portfolio optimization problem. Furthermore, an upside-chance maximization problem of a large deviation probability is stated as a ‘dual’ optimization problem. As an example, a ‘linear-quadratic’ model is studied in detail: the conditions to ensure the solvabilities of the problems are discussed and explicit expressions for the solutions are presented.

Keywords

Drawdown constraintrisk constraintlong-term investmentrisk-sensitive controlSkorokhod equationalgebraic Riccati equation

MSC classification

Primary: 93E20: Optimal stochastic control 90C39: Dynamic programming 49N10: Linear-quadratic problems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 3 , September 2006 , pp. 673 - 692
Copyright
Copyright © Applied Probability Trust 2006 

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