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Optimal consumption problem in the Vasicek model

Trybuła J.

Opuscula Mathematica

2015

Vol. 35, no. 4

547--560

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.

Optimal dividend policy in discrete time

Marciniak E., Trybuła J.

Demonstratio Mathematica

2014

Vol. 47, nr 1

258--270

A problem of optimal dividend policy for a firm with a bank loan is considered. A regularity of a value function is established. A numerical example of calculating value function is given.