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

Optimal Consumption in a Brownian Model with Absorption and Finite Time Horizon We construct ϵ -optimal strategies for the following control problem: Maximize $\mathbb {E}( \int_{(0,\tau)}e^{-\beta s}\,dC_{s}+e^{-\beta\tau}X_{\tau})$ , 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

, Volume 67 (2) – Apr 1, 2013
45 pages

/lp/springer_journal/optimal-consumption-in-a-brownian-model-with-absorption-and-finite-Xviamhucfs
Publisher
Springer Journals
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-012-9185-x
Publisher site
See Article on Publisher Site

Abstract

We construct ϵ -optimal strategies for the following control problem: Maximize $\mathbb {E}( \int_{(0,\tau)}e^{-\beta s}\,dC_{s}+e^{-\beta\tau}X_{\tau})$ , 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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2013

DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month Explore the DeepDyve Library Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve Freelancer DeepDyve Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations