The Effects of Largest Claims and Excess of Loss Reinsurance on a Company's Ruin Time and Valuation

Abstract: 

Joint work with Tiandong Wang (Cornell), Yuguang Fan (Melb.U.), Philip S. Griffin (Syracuse) and Alex Szimayer (Hamburg).

I'll report on some work in which we compare two types of reinsurance: excess of loss (EOL) and largest claim reinsurance (LCR), each of which transfers the payment of part or all of a large claim from the primary insurance company (the cedant) to a reinsurer, in some way.  The primary insurer's point of view is taken, for assessment of risk and calculation of the reinsurance premium payable.

Assuming the classical compound Poisson risk model with heavy, medium and light-tailed claim size distributions, simulations are used to illustrate the impact of the EOL and LCR treaties on the company's ruin probability, ruin time and overall value as measured by a dividend discounting model. 

We find pros and cons for the two types of reinsurance. LCR is more effective than EOL in averting ruin, but, correspondingly, costs more, at least  for small levels of initial capital. (For large levels of initial capital, the differences disappear.)  On the other hand, LCR reduces risk considerably over EOL, in a variety of situations, as measured by the variance of the company value. A further interesting finding from the simulations is that heaviness of tails alone is not necessarily the decisive factor in the possible ruin of a company; small and moderate sized claims can also play a significant role in this.