092048 (E10) The use of control-theoretic ideas for the distribution of bonus in non-life insurance : Martin-Löf A., Presented at the International Workshop on The Interplay between Insurance, Finance and Control, organized by the Mathematical Research Centre at Aarhus University, also supported by the Danish Science Research Council and the Centre for Analytical Finance

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 87 KB
• Volume: 20
• Category: Article
• ISSN: 0167-6687
• DOI: 10.1016/s0167-6687(97)80672-5

✦ Synopsis

Let a decision policy ~r correspond to a twodimensional stochastic process {tzlr(t), Lt'}, with 0 < tx~(t) _< 1 where 1-tx,( 0 denotes the fraction of the incoming claims at time t that is reinsured and L," denotes the total payout of dividend up to time t. When applying policy ~-the reserve of the insurance company R t" is governed by a SDE dRt'r =ot,r( t)pdt + o%( t)crdWt -dL T ,

where {WI} is a standard Brownian motion and/z,a > 0 are constants. The objective is then to find a policy that maximizes the return function V(x)=E ~" e-CtdLT, where c > 0 is a discount factor, T~r is tliJe°time of ruin and x refers to the initial reserve. Two cases are treated:

-The rate of dividend pay-out is bounded by some positive constant M.

-There is no restriction on the rate of dividend pay-out, that is {L ~'} assumed to be right-continuous with left limits. This is based on a joint work with Michael Taksar, SUNY, Stony Brook and generalizes a recent result by S. Asmussen & M. Taksar.