Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments. (30th January 2018)

• Record Type: Journal Article
• Authors: Hao, Xuemiao; Tang, Qihe
• Is Part Of: Journal of applied probability. Volume 49:Number 4(2012)
• Page Start: 939
• Page End: 953
• Publication Date: 2018-01-30
• Subjects: (extended) regular variation, -- finite-time and infinite-time ruin probabilities, -- Lévy process, -- stochastic difference equation, -- tail probability; 91B30, -- 60G51, -- 91B28; 519.2
• DOI: 10.1239/jap/1354716649
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y 0 = x > 0, evolves according to d Y t = Y t - d R t -d P t for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential of R fulfills a moment condition. We obtain a simple and unified asymptotic formula as x →∞, which confirms Paulsen's conjecture.