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Ruin Probability on Insurance Risk Models
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 Title & Authors
Ruin Probability on Insurance Risk Models
Park, Hyun-Suk; Choi, Jeong-Kyu;
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In this paper, we study an asymptotic behavior of the finite-time ruin probability of the compound Poisson model in the case that the initial surplus is large. To compare an exact ruin probability with an approximate one, we place the focus on the exact calculation for the ruin probability when the claim size distribution is regularly varying tailed (i.e. exponential claims and inverse Gaussian claims). We estimate an adjustment coefficient in these examples and show the relationship between the adjustment coefficient and the safety premium. The illustration study shows that as the safety premium increases so does the adjustment coefficient. Larger safety premium means lower "long-term risk", which only stands to reason since higher safety premium means a faster rate of safety premium income to offset claims.
Insurance risk model;ruin probability;regular variation;Lvy processes;
 Cited by
A compound Poisson risk model with variable premium rate,Song, Mi Jung;Kim, Jongwoo;Lee, Jiyeon;

Journal of the Korean Data and Information Science Society, 2012. vol.23. 6, pp.1289-1297 crossref(new window)
A compound Poisson risk model with variable premium rate, Journal of the Korean Data and Information Science Society, 2012, 23, 6, 1289  crossref(new windwow)
Bertoin, J. and Doney, R. A. (1994). Cramer's estimate for Levy processes, Statistics and Probability Letters, 21, 363-365. crossref(new window)

Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular Variation, Cambridge University Press.

Dickson, D. C. M. and Hipp, C. (2001). On the time to ruin for Erlang(2) risk processes, Insurance: Math-matics & Economics, 29, 333-344. crossref(new window)

Doney, R. A. and Kyprianou, A. (2006). Overshoots and undershoots of Levy processes, Annals of Applied Probability, 16, 91-106. crossref(new window)

Embrechts, P., Goldie, C. M. and Veraverbeke, N. (1979). Subexponentaility and infinite divisibility, Z.Wahrsch. Verw. Gebiete, 49, 335-347. crossref(new window)

Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer-Verlag, Berlin.

Goldie, C. M. (1978). Subexponential distributions and dominated-variation tails, Journal of Applied Probability, 15, 440-442. crossref(new window)

Kluppelberg, C., Kyprianou, A. E. and Maller, R. A. (2004). Ruin probabilities and overshoots for general Levy insurance risk processes, Annals of Applied Probability, 14, 1766-1801. crossref(new window)

Park, H. S. (2010). Computing the ruin probability of Levy insurance risk processes in non-Cramer models, Communications of the Korean Statistical Society, 17, 483-491. crossref(new window)

Park, H. S. (2011). A note on limiting distribution for jumps of Levy insurance risk model, Journal of the Korean Statistical Society, 40, 93-98. crossref(new window)

Park, H. S. and Maller, R. A. (2008). Moment and MGF convergence of overshoots and undershoots for Levy insurance risk processes, Advances in Applied Probability, 40, 716-733. crossref(new window)

Tang, Q. and Tsitsiashvili, G. (2003). Randomly weighted sums of subexponential random variables with application to ruin theory, Extremes, 6, 171-188. crossref(new window)

Teugels, J. L. (1975). The class of subexponential distributions, Annals of Probability, 3, 1000-1011. crossref(new window)