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

We construct ϵ -optimal strategies for the following control problem: Maximize , where X t = x + μt + σW t − C t , τ ≡inf{ t >0| X t =0}∧ T , T >0 is a fixed finite time horizon, W t is standard Brownian motion, μ , σ are constants, and C t describes accumulated consumption until time t . It i...

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Bibliographic Details
Published in:Applied mathematics & optimization 2013-04, Vol.67 (2), p.197-241
Main Author: Grandits, Peter
Format: Article
Language:English
Subjects:
ABSORPTION
Applied mathematics
Barriers
Boundary value problems
Brownian motion
BROWNIAN MOVEMENT
Calculus of Variations and Optimal Control
Optimization
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Constants
CONTROL
Endowment
Expected values
Horizon
Integral equations
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Simulation
Strategy
Studies
Systems Theory
Theoretical
TIME DEPENDENCE
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Summary:We construct ϵ -optimal strategies for the following control problem: Maximize , where X t = x + μt + σW t − C t , τ ≡inf{ t >0| X t =0}∧ T , T >0 is a fixed finite time horizon, W t is standard Brownian motion, μ , σ are constants, and C t describes accumulated consumption until time t . It is shown that ϵ -optimal strategies are given by barrier strategies with time-dependent barriers.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-012-9185-x