Abstract
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.
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References
Browne, 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)
Hipp, C., Plum, M.: Optimal investment for insurers. Insurance: Mathematics and Economics, 27, 215–228 (2000)
Gaier, J., Grandits, P., Schachermayer, W.: Asymptotic ruin probability and optimal investment. Annals of Applied Probability, 13, 1054–1076 (2003)
Hipp, C., Schmidli, H.: Asymptotics of ruin probabilities for controlled risk processes in the small claims case. Scandinavian Actuarial Journal, 5, 321–335 (2004)
Yang, H., Zhang, L.: Optimal investment for insurer with jump-diffusion risk process. Insurance: Mathematics and Economics, 37, 615–634 (2005)
Baev, 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)
Liang, 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)
Cox, J. C., Ingersoll, J. E., Ross, S. A.: A theory of the term structure of interest rates. Econometrica, 53, 385–407 (1985)
Wang, Z.: General Theorems of Stochastic Processes (in Chinese), Beijing Normal University Publishing Company, Beijing, 1965
Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North-Holland Publishing Company, New York, 1989
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Supported by National Basic Research Program of China (973 Program, Grant No. 2007CB814905) and National Natural Science Foundation of China (Grant No. 10871102) fication 91B30, 60H30
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Li, J.Z., Wu, R. Upper bounds for ruin probabilities under stochastic interest rate and optimal investment strategies. Acta. Math. Sin.-English Ser. 28, 1421–1430 (2012). https://doi.org/10.1007/s10114-012-0153-9
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DOI: https://doi.org/10.1007/s10114-012-0153-9
Keywords
- Cox-Ingersoll-Ross model
- jump-diffusion model
- optimal investment
- Ornstein-Uhlenbeck (O-U) process
- ruin probability
- stochastic interest rate