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Arbitrage Theory in Continuous Time$
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Tomas Björk

Print publication date: 2004

Print ISBN-13: 9780199271269

Published to Oxford Scholarship Online: October 2005

DOI: 10.1093/0199271267.001.0001

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Stochastic Optimal Control

Stochastic Optimal Control

(p.271) 19 Stochastic Optimal Control
Arbitrage Theory in Continuous Time

Tomas Björk (Contributor Webpage)

Oxford University Press

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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