Approximations for optimal stopping of a piecewise-deterministic process |
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Authors: | O L V Costa M H A Davis |
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Affiliation: | (1) Department of Electrical Engineering, Imperial College, SW7 2BT London, England |
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Abstract: | This paper deals with approximation techniques for the optimal stopping of a piecewise-deterministic Markov process (P.D.P.).
Such processes consist of a mixture of deterministic motion and random jumps. In the first part of the paper (Section 3) we
study the optimal stopping problem with lower semianalytic gain function; our main result is the construction of ε-optimal
stopping times. In the second part (Section 4) we consider a P.D.P. satisfying some smoothness conditions, and forN integer we construct a discretized P.D.P. which retains the main characteristics of the original process. By iterations of
the single jump operator from ℝ
N
to ℝ
N
, each iteration consisting ofN one-dimensional minimizations, we can calculate the payoff function of the discretized process. We demonstrate the convergence
of the payoff functions, and for the case when the state space is compact we construct ε-optimal stopping times for the original
problem using the payoff function of the discretized problem. A numerical example is presented. |
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Keywords: | Optimal stopping Piecewise-deterministic processes Optimal stochastic control Approximation techniques Dynamic programming |
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