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The aim of this paper is to study the risk of misspecifying solvency models for insurance companies. Based on a basic solvency model, we examine the sensitivity of different risk measures with respect to model misspecification. Our analysis considers the effects of introducing stochastic jumps and linear, as well as non-linear dependencies into the basic setting on the solvency capital requirements, shortfall probability and expected policyholder deficit. The simulation results suggest that the sensitivity of solvency capital as a risk measure - as it is in regulatory practice - underestimate the actual misspecification risk that policyholders are exposed to. We also find that mandatory interim reports can significantly reduce the model uncertainty faced by a regulator. This has important implications for the design of risk-based capital standards and the implementation of internal solvency models. Finally, pooling effects in insurance are discussed.

We present a few known results and many open problems on "practical" ruin probability approximations. The approximation of nonnegative random variables by combinations of exponentials is one of the bread and butter problems of applied probability. One natural approach is to obtain first RLT's (rational approximations of its Laplace transform), which may be easily achieved by modern symbolic-numeric software.The inversion of these RLT's yields then in combinations of exponentials, trigonometric and polynomial functions. While easy to implement, this approach has the essential drawback, when applied in probability, of failing to guarantee "feasible" approximations (i.e. nonnegative densities or nonincreasing cdf's), which is a quite challenging problem.