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Bounded Variation Control of Itô Diffusions with Exogenously Restricted Intervention Times

Part of: Miscellaneous topics in calculus of variations and optimal control Stochastic processes Stochastic systems and control Markov processes

Published online by Cambridge University Press:  22 February 2016

Jukka Lempa
Jukka Lempa*
Affiliation:
Oslo and Akershus University College
*
∗ Postal address: School of Business, Faculty of Social Sciences, Oslo and Akershus University College, PO Box 4, St. Olavs Plass, 0130 Oslo, Norway. Email address: jukka.lempa@hioa.no
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Abstract

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In this paper, bounded variation control of one-dimensional diffusion processes is considered. We assume that the agent is allowed to control the diffusion only at the jump times of an observable, independent Poisson process. The agent's objective is to maximize the expected present value of the cumulative payoff generated by the controlled diffusion over its lifetime. We propose a relatively weak set of assumptions on the underlying diffusion and the instantaneous payoff structure, under which we solve the problem in closed form. Moreover, we illustrate the main results with an explicit example.

Keywords

Bounded variation controlItô diffusionPoisson processresolvent operatorsingular stochastic control

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 60J60: Diffusion processes 49N25: Impulsive optimal control problems 60G40: Stopping times; optimal stopping problems; gambling theory

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 46 , Issue 1 , March 2014 , pp. 102 - 120
Copyright
© Applied Probability Trust 

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