Large deviations for the stochastic present value of aggregate net claims with infinite variance in the renewal risk model and its application in risk management
- 160 Downloads
In insurance, if the insurer continuously invests her wealth in risk-free and risky assets, then the price process of the investment portfolio can be described as a geometric present Lévy process. People always are interested in estimating the tail distribution of the stochastic present value of aggregate claims. In this paper, the large deviation for the stochastic present value of aggregate net claims, when the net claim size distribution is of Pareto type with finite expectation are obtained. We conduct some simulations to check the accuracy of the result we obtained and consider a portfolio optimization problem that maximizes the expected terminal wealth of the insurer subject to a solvency constraint.
KeywordsLarge deviations Regular variation Exponential Lévy process
This work was partially supported by the National Natural Science Foundation of China (Grant No. 71671166) and the Talent start-up fund of China Three Georges University (Grant No. 1910103).
- 5.Nagaev, A.V.: Limit theorems for large deviations when Cramér’s conditions are violated. Fiz-Mat. Nauk. 7, 17–22 (1969b) (in Russian)Google Scholar
- 7.Cline, D.B.H., Hsing, T.: Large deviation probabilities for sums and maxima of random variables with heavy or subexponential tails. Texas A & M University (1991) (Preprint)Google Scholar
- 20.Zhou, Q., Luo, J.: Artificial neural network based grid computing of E-government scheduling for emergency management. Comput. Syst. Sci. Eng. 30(5), 327–335 (2015)Google Scholar
- 24.Zhou, Q., Luo, J.: The study on evaluation method of urban network security in the big data era. Intell. Autom. Soft Comput. (2017). doi: 10.1080/10798587.2016.1267444