## Discrete time optimal dividend problem with constant premium and exponentially distributed claims

### Volume 41 / 2014

Applicationes Mathematicae 41 (2014), 13-31
MSC: Primary 90C40; Secondary 90C46.
DOI: 10.4064/am41-1-2

#### Abstract

\looseness 2 An optimal dividend problem is studied consisting in maximisation of expected discounted dividend payments until ruin time. A solution of this problem for constant premium $d$ and exponentially distributed claims is presented. It is shown that an optimal policy is a barrier policy. Moreover, an analytic way to solve this problem is sketched.