Abstract
The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims.
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References
Asmussen S, Højgaard B. Approximations for finite horizon ruin probabilities in the renewal model. Scand Actuar J, 1999: 106–119 (1999)
Avram F, Usábel M. Ruin probabilities and deficit for the renewal risk model with phase-type interarrival times. Astin Bull, 34: 315–332 (2004)
Cossette H, Landriault D, Marceau E. Ruin probabilities in the discrete time renewal risk model. Insurance Math Econom, 38: 309–323 (2006)
Stanford D A, Avram F, Badescu A L, et al. Phase-type approximations to finite-time ruin probabilities in the Sparre-Andersen and stationary renewal risk models. Astin Bull, 35: 131–144 (2005)
Thorin O. On the asymptotic behavior of the ruin probability for an infinite period when the epochs of claims form a renewal process. Scand Actuar J, 1994: 81–99 (1974)
Chen Y, Ng K W. The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims. Insurance Math Econom, 40: 415–423 (2007)
Frolova A, Kabanov Y, Pergamenshchikov S. In the insurance business risky investments are dangerous. Finance Stoch, 6: 227–235 (2002)
Tang Q. Heavy tails of discounted aggregate claims in the continuous-time renewal model. J Appl Probab, 44: 285–294 (2007)
Tang Q, Tsitsiashvili G. Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments. Adv Appl Probab, 36: 1278–1299 (2004)
Tang Q, Tsitsiashvili G. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Process Appl, 108: 299–325 (2003)
Klüuppelberg C, Mikosch T. Large deviations of heavy-tailed random sums with applications in insurance and finance. J Appl Probab, 34: 293–308 (1997)
Ng K W, Tang Q, Yan J, et al. Precise large deviations for the prospective-loss process. J Appl Probab, 40: 391–400 (2003)
Tang Q, Su C, Jiang T, et al. Large deviations for heavy-tailed random sums in compound renewal model. Statist Probab Lett, 52: 91–100 (2001)
Goldie C M. Subexponential distributions and dominated-variation tails. J Appl Probab, 15: 440–442 (1978)
Bingham N H, Goldie C M, Teugels J L. Regular Variation. Cambridge: Cambridge University Press, 1987
Embrechts P, Klüppelberg C, Mikosch T. Modelling Extremal Events for Insurance and Finance. Berlin: Springer-Verlag, 1997
Dufresne D. The distribution of a perpetuity, with applications to risk theory and pension funding. Scand Actuar J, 1990: 39–79 (1990)
Cline D B H, Samorodnitsky G. Subexponentiality of the product of independent random variables. Stochastic Process Appl, 49: 75–98 (1994)
Gjessing H K, Paulsen J. Present value distributions with applications to ruin theory and stochastic equations. Stochastic Process Appl, 71: 123–144 (1997)
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This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the Research Grant of Renmin University of China (Grant No. 08XNA001)
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Wei, L. Ruin probability of the renewal model with risky investment and large claims. Sci. China Ser. A-Math. 52, 1539–1545 (2009). https://doi.org/10.1007/s11425-009-0053-3
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DOI: https://doi.org/10.1007/s11425-009-0053-3