Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments
School of Finance, Renmin University of China, 59 Zhongguancun Street, Haidian District, Beijing 100872, China
Department of Mathematics, University of St. Thomas—Minnesota, 2115 Summit Avenue, St. Paul, MN 55105, USA
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
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
consisting of stochastic discount factors of the d
financial assets invested. To capture both heavy tails and asymptotic dependence of
in an integrated manner, we assume that
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
are independent with X
of Fréchet type; (ii) X
are independent with X
of Gumbel type; (iii) X
jointly possess a standard MRV structure; (iv) X
jointly possess a nonstandard MRV structure.
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).
Share & Cite This Article
MDPI and ACS Style
Liu, J.; Zhang, H. Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments. Risks 2017, 5, 28.
Liu J, Zhang H. Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments. Risks. 2017; 5(2):28.
Liu, Jing; Zhang, Huan. 2017. "Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments." Risks 5, no. 2: 28.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
Multiple requests from the same IP address are counted as one view.