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

Gaier, Johanna; Grandits, Peter

Insur. Math. Econ. 30, No. 2, 211-217 (2002).

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.

MSC:

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

Keywords:

Optimal investment; Ruin probabilities; Regular variation

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