Ruin probabilities in the presence of regularly varying tails and optimal investment. (English) Zbl 1055.91049

Summary: We study the infinite time ruin probability in the classical Cramer-Lundberg model, where the company is allowed to invest their money in a stock, which is described by geometric Brownian motion. Starting from an integro-differential equation for the maximal survival probability, we analyze the case of claim sizes, which have distribution functions \(F\) with regularly varying tails. Our result is: if \(1-F\) is regularly varying with index \(\rho<-1\), then the ruin probability \(\psi\) is also regularly varying with index \(\rho<-1\). This holds under the assumption of zero interest rates.


91B30 Risk theory, insurance (MSC2010)
91B28 Finance etc. (MSC2000)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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