Asymptotic Estimates of the Ruin Probability for an Insurer

01.08.2002 - 31.07.2005
Research funding project
The ruin probability of a company is the probability that the wealth of the company falls below zero at some future time. The wealth process of a typical insurance company is described by the claims it incurs and by its premium income. Since 1903, when F. Lundberg introduced a collective risk model based on a homogeneous Poisson claim process, the calculation of ruin probabilities in this setting has been very well understood . It is known that, if the claim sizes have exponential moments, the ruin probability decreases exponentially with the initial wealth. Also if the claim sizes have heavier tails, there exist numerous results in the literature. The overall aim of this project is to generalize these results to a setting where besides the risk process there exists some investment possibility, e.g. described by geometric Brownian motion. Then the insurer should have the possibility to reduce his ruin probability by choosing good investment strategies. In particular we want to investigate the asymptotic behaviour of the minimal ruin probability for large claims, when the distribution function of the claim sizes is of regular variation. Another goal of the project will be to look at the minimal ruin probability for small claims with exponential moments. We will use martingale methods to deduce Cramér-Lundberg bounds and asymptotics and to derive some information about the optimal investment strategy leading to the minimal ruin probability. Furthermore economically reasonable generalizations will be looked at, like the introduction of interest rates and dividend barriers. The results of the project shall provide valuable information for insurers or other companies with stochastic risks about opportunities and risks arising from investment possibilities. This is in line with the present emphasis - in practice as well as in theory - on asset-liability management, i.e., the consideration of risks on the liability side as well as on the asset side of the balance sheet.

People

Project leader

Institute

Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Keywords

GermanEnglish
Ruinwahrscheinlichkeitruin probability
Investmentinvestment
Martingal Methodenmartingale methods

External partner

  • Sveučili¿te u Zagrebu

Publications