Statistical analysis of mixtures underlying probability of ruin

Abstract

If the hypothesis on exponentially distributed claims in a risk (or surplus) model is untenable then, in many cases, the assumption that they are mixtures of two (or more) exponentials is a suitable substitute. In the first part of the paper tests of homogeneity for exponentially distributed claims are discussed and their properties are stated. The statistical properties of parameter estimations for such claims are also mentioned. In the second part the classical Cramer-Lundberg ruin model is discussed when claims are distributed as mixtures of exponentials. Our attention is focussed primarily on assesment of accuracy of approximations obtained. Then our results are compared to those already known.

On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

“…Recall that the ruin probability for a mixture of exponentials is given, e.g. in Potocký and Stehlík (2009). The case where the risk model is infl uenced by a constant interest rate is treated, e.g.…”