Optimal Consumption in a Brownian Model with Absorption and Finite Time Horizon

Journal Article · Mon Apr 15 00:00:00 EDT 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-012-9185-X· OSTI ID:22156413

Grandits, Peter ^[1]

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1. TU Wien, Institut fuer Wirtschaftsmathematik (Austria)

We construct {epsilon}-optimal strategies for the following control problem: Maximize E[{integral}{sub [0,{tau})}e{sup -{beta}s} dC{sub s}+e{sup -{beta}{tau}}X{sub {tau}}] , where X{sub t}=x+{mu}t+{sigma}W{sub t}-C{sub t}, {tau}{identical_to}inf{l_brace}t>0|X{sub t}=0{r_brace} Logical-And T, T>0 is a fixed finite time horizon, W{sub t} is standard Brownian motion, {mu}, {sigma} are constants, and C{sub t} describes accumulated consumption until time t. It is shown that {epsilon}-optimal strategies are given by barrier strategies with time-dependent barriers.

• OSTI ID: 22156413
• Journal Information: Applied Mathematics and Optimization, Vol. 67, Issue 2; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ABSORPTION
BROWNIAN MOVEMENT
CONTROL
TIME DEPENDENCE