We consider the problem of an insurer who decides to allocate a proportion (1 - a(t)) of premiums to a re-insurance company (thereby retaining a proportion a(t) of premiums). The insurer also has to pay dividends c(t) at any time t to shareholders. If the insurer's reserve is x(t) given by the modi ed Cramer- Lundberg model that allows jumps, we solve a dual optimal policy of a dividend payout scheme for shareholders with constant relative risk aversion (CRRA) preferences and retention level of received premiums for the insurance company . We set the problem as a stochastic control problem and solve the resulting HJB equation . We nd that the optimal risk level and dividend payout can never depend on time. Other important results are discussed in detail.
Dr. Sure Mataramvura is a senior Lecturer in the Department of Actuarial Science, University of Cape Town. Holds a Ph.D in Financial Mathematics and researches in the field of Investments, Derivative Pricing, Insurance Mathematics, Stochastic Calculus and Computational Finance. Supervised and graduated 5 Ph.D students and supervising 2 more. Supervised more than 15 Masters students. Involved in AIMS (African Institute of Mathematics Sciences) collaborations which include AIMS Ghana, AIMS South Africa, AIMS Tanzania and AIMS Senegal. Also a member and one time Secretary of SAMSA (Southern Africa Mathematical Sciences Association) which promotes research and collaborations between researchers and students in Africa and the rest of the world.