Modeling and Management of Nonlinear Dependencies - Copulas in Dynamic Financial Analysis

The aim of this paper is to study the influence of nonlinear dependencies on a nonlife
insurers risk and return profile. To achieve this, we integrate several copula
models in a dynamic financial analysis (DFA) framework and conduct numerical
tests within a simulation study. We also test several risk management strategies in
response to adverse outcomes generated by nonlinear dependencies. We find that
nonlinear dependencies have a crucial influence on the insurers risk profile that can
hardly be affected by the analyzed management strategies. Depending on the copula
concept employed, we find large differences in risk assessment for the ruin
probability and for the expected policyholder deficit. This has important implications
for regulators and rating agencies that use these risk measures as a foundation
for capital standards and ratings.