DSpace Repository :: Browsing by Subject "stochastic control"

Article

Open Access

A direct approach to linear-quadratic stochastic control

(Wydawnictwa AGH, 2017) Duncan, Tyrone E.; Pasik-Duncan, Bozenna

A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.

Article

Open Access

Optimal consumption problem in the Vasicek model

(2015) Trybuła, Jakub

We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumption strategy and the value function.