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Arbitrage Theory in Continuous Time$
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Arbitrage Theory in Continuous Time

Tomas Björk

Print publication date: 2004

Print ISBN-13: 9780199271269

Published to Oxford Scholarship Online: October 2005

DOI: 10.1093/0199271267.001.0001

Stochastic Optimal Control

Chapter:
(p. 271 ) 19 Stochastic Optimal Control
Source:
Arbitrage Theory in Continuous Time
Author(s):

Tomas Björk (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0199271267.003.0019

This chapter analyses the stochastic optimal control problem. The problem considers an economic agent over a fixed time interval [0, T]. At time t = 0, the agent is endowed with initial wealth x0, and the agent’s problem is how to allocate investments and consumption over the given time horizon. The agent must choose a portfolio-consumption strategy that will maximize the total utility over [0, T]. Practice exercises are included.

Keywords:   stochastic optimal control problem, portfolio consumption, investment, dynamic programming

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