Optimal Allocation of Policy Layers for Exponential Risks

Abstract

In this paper, we study the problem of optimal allocation of insurance layers for a portfolio of i.i.d exponential risks. Using the first stochastic dominance criterion, we obtain an optimal allocation for the total retain risks faced by a policyholder. This result partially generalizes the known result in the literature for deductible as well as policy limit coverages.

Lower and upper bounds for survival functions of the smallest and largest claim amounts in layer coverages

“…We know that X 1 ≤ rh X 2 ≤ rh X 3 . In Figure 1, we plot the survival function of max 1≤i≤n {X i (d π i , d π i + l τ i ]} where (l 1 , l 2 , l 3 ) = (10, 20, 30), (d 1 , d 2 , d 3 ) = (3,6,9) and (π 1 , π 2 , π 3 ) and (τ 1 , τ 2 , τ 3 ) are permutations of (1,2,3). It is seen that the survival function of…”