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Optimal stochastic control without convexity conditions in the dynamical equation

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Abstract

The stochastic control system studied is modelled by then-dimensional stochastic differential equation

$$dz_t = f(t, z, u) dt + \sigma (t, z) dW_t ,$$

whereW t isn-dimensional Brownian motion andu takes its values in a setU υR m. We prove the existence of a controlu*(t,z) which minimizes the cost functional

$$E\int_0^T {c(t, z, u) dt,} $$

under mild conditions off and σ, and without requiring thatf(t,z,U) be convex for each (t,z) or thatU be compact.

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Authors and Affiliations

  1. Department of Mathematics, Sir George Williams Campus, Concordia University, Montreal, Québec, Canada

    A. Boyarsky (Associate Professor)

Authors
  1. A. Boyarsky
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Additional information

Communicated by G. Leitmann

This research was supported by the National Research Council of Canada, Grant No. A9072.

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Boyarsky, A. Optimal stochastic control without convexity conditions in the dynamical equation. J Optim Theory Appl 20, 481–488 (1976). https://doi.org/10.1007/BF00933132

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  • DOI: https://doi.org/10.1007/BF00933132

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