Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 25 (2020), paper no. 11, 12 pp.
A note on costs minimization with stochastic target constraints
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.
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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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