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Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments

Jing Liu () and Huan Zhang ()
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Jing Liu: School of Finance, Renmin University of China, 59 Zhongguancun Street, Haidian District, Beijing 100872, China
Huan Zhang: Department of Mathematics, University of St. Thomas—Minnesota, 2115 Summit Avenue, St. Paul, MN 55105, USA

Risks, 2017, vol. 5, issue 2, 1-11

Abstract: Motivated by the EU Solvency II Directive, we study the one-year ruin probability of an insurer who makes investments and hence faces both insurance and financial risks. Over a time horizon of one year, the insurance risk is quantified as a nonnegative random variable X equal to the aggregate amount of claims, and the financial risk as a d -dimensional random vector Y consisting of stochastic discount factors of the d financial assets invested. To capture both heavy tails and asymptotic dependence of Y in an integrated manner, we assume that Y follows a standard multivariate regular variation (MRV) structure. As main results, we derive exact asymptotic estimates for the one-year ruin probability for the following cases: (i) X and Y are independent with X of Fréchet type; (ii) X and Y are independent with X of Gumbel type; (iii) X and Y jointly possess a standard MRV structure; (iv) X and Y jointly possess a nonstandard MRV structure.

Keywords: asymptotics; Breiman’s theorem; max-domain of attraction; multivariate regular variation; ruin probability (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2017
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