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Recursive calculation of time to ruin distributions. (English) Zbl 1074.91545
Summary: We present a different approach on D. C. M. Dickson and H. R. Waters [Astin Bull. 21, 199–221 (1991)] and F. De Vylder and M. I. Goovaerts [Insur. Math. Econ. 7, No. 1, 1–7 (1988; Zbl 0629.62101)] methods to approximate time to ruin probabilities. By means of Markov chain application we focus on the direct calculation of the distribution of time to ruin, and we find that the above recursions appear to be less efficient, although giving the same approximation figures. We show some graphs of the time to ruin distribution for some examples, comparing the different shapes of the densities for different values of the initial surplus. Furthermore, we consider the presence of an upper absorbing barrier and apply the proposed recursion to find ruin probabilities in this case.

MSC:
91B30 Risk theory, insurance (MSC2010)
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References:
[1] De Vylder, F.; Goovaerts, M.J., Recursive calculation of finite time ruin probabilities, Insurance: mathematics and economics, 7, 1-7, (1988) · Zbl 0629.62101
[2] Dickson, D.C.M., Gray, J.R., 1984. Approximations to ruin probability in the presence of an upper absorbing barrier. Scandinavian Actuarial Journal, 105-115. · Zbl 0584.62174
[3] Dickson, D.C.M.; Waters, H.R., Recursive calculation of survival probabilities, Astin bulletin, 21, 199-221, (1991)
[4] Dickson, D.C.M.; Egı́dio dos Reis, A.D.; Waters, H.R., Some stable algorithms in ruin theory and their applications, Astin bulletin, 25, 153-175, (1995)
[5] Panjer, H.H., Recursive evaluation of a family of compound distributions, Astin bulletin, 12, 22-26, (1981)
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