Consider the problem of approximating the tail probability of randomly weighted sums and their maxima, where {Xi,i=1} is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class, and {[Theta]i,i=1} is a sequence of...

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...

The multivariate regular variation (MRV) is one of the most important tools in modeling multivariate heavy-tailed phenomena. This paper characterizes the MRV distributions through the tail dependence function of the copula associated with them. Along with some existing results, our studies...

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...

In this paper, the Conditional Value-at-Risk (CVaR) is adopted to measure the total loss of multiple lines of insurance business and two nonparametric estimation methods are introduced to explore the optimal multivariate quota-share reinsurance under a mean-CVaR framework. While almost all the...