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

by 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
Risks 2017, 5(2), 28; https://doi.org/10.3390/risks5020028
Received: 28 March 2017 / Revised: 22 April 2017 / Accepted: 22 April 2017 / Published: 6 May 2017
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
MDPI and ACS Style

Liu, J.; Zhang, H. Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments. Risks 2017, 5, 28. https://doi.org/10.3390/risks5020028

AMA Style

Liu J, Zhang H. Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments. Risks. 2017; 5(2):28. https://doi.org/10.3390/risks5020028

Chicago/Turabian Style

Liu, Jing, and Huan Zhang. 2017. "Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments" Risks 5, no. 2: 28. https://doi.org/10.3390/risks5020028

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