Upper Bounds for Ruin Probabilities under Stochastic Interest Rate and Optimal Investment Strategies 被引量：2

Upper Bounds for Ruin Probabilities under Stochastic Interest Rate and Optimal Investment Strategies

导出

摘要 In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method. In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.

作者 Jin Zhu LI Rong WU

机构地区 School of Mathematical Sciences and LPMC

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第7期1421-1430,共10页 数学学报（英文版）

基金 Supported by National Basic Research Program of China (973 Program, Grant No. 2007CB814905) National Natural Science Foundation of China (Grant No. 10871102)

关键词 Cox Ingersoll-Ross model jump-diffusion model optimal investment Ornstein Uhlen- beck （O-U） process ruin probability stochastic interest rate Cox Ingersoll-Ross model, jump-diffusion model, optimal investment, Ornstein Uhlen- beck （O-U） process, ruin probability, stochastic interest rate

分类号 O211.6 [理学—概率论与数理统计]

引文网络
相关文献

参考文献10

1Browne, S.: Optimal investment policies for a firm with random risk process: exponential utility and minimizing the probability of ruin. Mathematics of Operations Research, 20, 937-958 (1995).
2Hipp, C., Plum, M.: Optimal investment for insurers. Insurance: Mathematics and Economics, 27, 215-228 (2000).
3Gaier, J., Grandits, P., Schachermayer, W.: Asymptotic ruin probability and optimal investment. Annals of Applied Probability, 13, 1054-1076 (2003).
4Hipp, C., Schmidli, H.: Asymptotics of ruin probabilities for controlled risk processes in the small claims case. Scandinavian Actuarial Journal, 5, 321-335 (2004).
5Yang, H., Zhang, L.: Optimal investment for insurer with jump-diffusion risk process. Insurance: Mathematics and Economics, 37, 615-634 (2005).
6Baev, A. V., Bondarev, B. V.: On the ruin probability of an insurance company dealing in a BS-market. Theory of Probability and Mathematical Statistics, 74, 11-23 (2007).
7Liang, Z., Guo, J.: Upper bound for ruin probabilities under optimal investment and proportional reinsurance. Applied Stochastic Model in Business and Industry, 24, 109-128 (2008).
8Cox, J. C., Ingersoll, J. E., Ross, S. A.: A theory of the term structure of interest rates. Econometriea, 53, 385-407 (1985).
9Wang, Z.: General Theorems of Stochastic Processes (in Chinese), Beijing Normal University Publishing Company, Beijing, 1965.
10Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North-Holland Publishing Company, New York, 1989.