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On a Non-Linear Differential-Integral Equation

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Abstract

Exact analytical solutions to a non-linear differential-integral equation that appears in a stochastic optimal control problem are given. The equation is satisfied by the value function in the control problem, from which the optimal control follows at once. Without the integral, the equation reduces to a Riccati differential equation.

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ACKNOWLEDGMENTS

This research was supported by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-ville, H3C 3A7, Montréal, Canada

    Mario Lefebvre

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  1. Mario Lefebvre
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Correspondence to Mario Lefebvre.

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(Submitted by T. K. Yuldashev)

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Lefebvre, M. On a Non-Linear Differential-Integral Equation. Lobachevskii J Math 43, 3216–3221 (2022). https://doi.org/10.1134/S1995080222140244

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