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Bounded variation control of Itô diffusions with exogenously restricted intervention times. (English) Zbl 1286.93204

Summary: 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.

MSC:

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

References:

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