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Risks 2017, 5(2), 28; doi:10.3390/risks5020028

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

1
and
2,3,*
1
School of Finance, Renmin University of China, 59 Zhongguancun Street, Haidian District, Beijing 100872, China
2
Department of Mathematics, University of St. Thomas—Minnesota, 2115 Summit Avenue, St. Paul, MN 55105, USA
3
Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Qihe Tang
Received: 28 March 2017 / Revised: 22 April 2017 / Accepted: 22 April 2017 / Published: 6 May 2017
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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. View Full-Text
Keywords: asymptotics; Breiman’s theorem; max-domain of attraction; multivariate regular variation; ruin probability asymptotics; Breiman’s theorem; max-domain of attraction; multivariate regular variation; ruin probability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Liu, J.; Zhang, H. Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments. Risks 2017, 5, 28.

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