092049 (E12, B22) The value of private safety versus the value of public safety : Johannesson M., Johansson P.O., O'Connor R.M., Journal of Risk and Uncertainty, Number 3, 1996, pp.263–275

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 87 KB
• Volume: 20
• Category: Article
• ISSN: 0167-6687
• DOI: 10.1016/s0167-6687(97)80671-3

✦ 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.