In this paper, we consider the survival probability for a two-dimensional risk model. We derive a partial integro-differential equation satisfied by the survival probability and prove its differentiability. We obtain explicit expressions for recursively calculating the survival probability by...

Let X denote the loss initially assumed by an insurer. In a reinsurance design, the insurer cedes part of its loss, say f(X), to a reinsurer, and thus the insurer retains a loss If(X)=X-f(X). In return, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the...

By formulating a constrained optimization model, we address the problem of optimal reinsurance design using the criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk. For completeness, we analyze the optimal reinsurance model under both binding...