Ruin probability for Lévy risk process compounded by geometric Brownian motion

Xianghua Zhao; Chuancun Yin

doi:10.1007/s11464-007-0021-6

Front. Math. China ›› 2007, Vol. 2 ›› Issue (2) : 317 -327. DOI: 10.1007/s11464-007-0021-6

Research Article

Ruin probability for Lévy risk process compounded by geometric Brownian motion

Xianghua Zhao ¹^,^a
, Chuancun Yin ¹

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Abstract

In this paper, we assume that the surplus of an insurer follows a Lévy risk process and the insurer would invest its surplus in a risky asset, whose prices are modeled by a geometric Brownian motion. It is shown that the ruin probabilities (by a jump or by oscillation) of the resulting surplus process satisfy certain integro-differential equations.

Keywords

Lévy risk process / geometric Brownian motion / ruin probability

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Xianghua Zhao, Chuancun Yin. Ruin probability for Lévy risk process compounded by geometric Brownian motion. Front. Math. China, 2007, 2(2): 317-327 DOI:10.1007/s11464-007-0021-6

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