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On a stochastic control problem with exit constraints

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Abstract

In this paper the logarithmic transformation of Fleming [1] is used to discuss a specific problem of controlled diffusions. The problem is to minimize a certain quadratic functional of the applied drift while satisfying the requirement that the place where the process exits a domain is not in a specified subset of its boundary. The main result is that the solution of this problem is given by the logarithm of a related exit probability.

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References

  1. W. H. Fleming, Exit Probabilities and Optimal Stochastic Control,Appl. Math. and Opt.,4, 329–346 (1978).

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  2. W. H. Fleming and R. W. Rishel,Deterministic and Stochastic Optimal Control, Springer-Verlag, 1975.

  3. D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1977.

  4. H. P. McKean,Stochastic Integrals, Academic Press, 1969.

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Authors and Affiliations

  1. Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, 02912, Providence, Rhode Island, USA

    Martin Day

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  1. Martin Day
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Additional information

Communicated by W. Fleming

This research was supported in part by the Air Force Office of Scientific Research under AF-AFOSR 76-3063.

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Day, M. On a stochastic control problem with exit constraints. Appl Math Optim 6, 181–188 (1980). https://doi.org/10.1007/BF01442892

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  • DOI: https://doi.org/10.1007/BF01442892

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