No coin nor oath required. For personal study only.
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.
📜 SIMILAR VOLUMES
The problem of determining optimal retention levels for a non-life portfolio consisting of a number of independent sub-portfolios was first discussed by de Finetti (1946). He considered retention levels to be optimal if they minimized the variance of the insurer's profit from the portfolio subject t
In this article, the authors discuss mixed exponential distributions and, more generally, scale mixtures with specific consideration the purpose of insurance modeling. Results are derived for equilibrium distributions (defined via stop-loss transforms) of mixed distributions. Some recursive relation
By taking the relevant expectations, the model yields a complete initial term structure for the continuum of maturities, endogenously interpolating between the observed data. Thus it is more parsimonious in its assumptions in the sense that there is no need for an exogenous interpolation rule and th