Associated people

J. Schröder, R. Niekamp, D. Brands, C. Götzen, M. Kiseleva, J. Niekamp, O. Siems

Abstract

Due to the European directive 'Solvency II' insurance companies need to estimate the possible claims for their individual portfolio for a 200 year event. The total loss amount includes estimations for losses suffered from natural catastrophes such as windstorms. For this task there exist a couple of commercial tools. Theyare based on physical models of wind appearance or they just work with distortions of historical hazards. In contrast to the approaches of the existing commercial simulation tools we develop in this project a purely data driven model. From the available historical data we extracted the hourly wind peeks measured at 400 weather stations in Central Europe over the last two decades. After a normalization of these data, removing the geographical exposure of the measure points, we generated a set of uncorrelated wind fields.
These wind fields are used to get a Polynomial Chaos expansion of the stochastic wind field by a recombination of these fields with stochastic coefficients. The stochastic coefficients themselves are constructed by multi-variate Hermite-polynomials with unknown deterministic coefficients. The equations for these latter coefficients are found by forcing the identity of a suitable set of mixed moments of the wind history and the stochastic model. The Quasi-Newton method is used to solve the arising highly non-linear equations.arising highly non-linear equations. The generation of the random wind-events with this stochastic model is computational very cheap. In the time scale of hours we can, using the Monte Carlo method, simulate 10^9 years of insurance risk due to wind hazards.