Electronic Communications in Probability

A note on costs minimization with stochastic target constraints

Yan Dolinsky, Benjamin Gottesman, and Gurel-Gurevich Ori

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We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi-linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.

Article information

Electron. Commun. Probab., Volume 25 (2020), paper no. 11, 12 pp.

Received: 26 November 2019
Accepted: 27 January 2020
First available in Project Euclid: 30 January 2020

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Primary: 49J15: Optimal control problems involving ordinary differential equations 60H30: Applications of stochastic analysis (to PDE, etc.) 93E20: Optimal stochastic control

optimal stochastic control backward stochastic differential equations

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Dolinsky, Yan; Gottesman, Benjamin; Ori, Gurel-Gurevich. A note on costs minimization with stochastic target constraints. Electron. Commun. Probab. 25 (2020), paper no. 11, 12 pp. doi:10.1214/20-ECP295. https://projecteuclid.org/euclid.ecp/1580353229

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