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Volumn 64, Issue 1, 1996, Pages 103-125

Large deviations results for subexponential tails, with applications to insurance risk

Author keywords

Conditioned limit theorem; Downwards skip free process; Excursion; Extreme value theory; Insurance risk; Integrated tail; Maximum domain of attraction; Path decomposition; Random walk; Regular variation; Ruin probability; Subexponential distribution

Indexed keywords


EID: 0030295610     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(96)00087-7     Document Type: Article
Times cited : (82)

References (42)
  • 1
    • 0001051380 scopus 로고
    • How large delays build up in a GI/GI/1 queue
    • V. Anantharam, How large delays build up in a GI/GI/1 queue, Queueing Systems 5 (1988) 345-368.
    • (1988) Queueing Systems , vol.5 , pp. 345-368
    • Anantharam, V.1
  • 2
    • 0001392225 scopus 로고
    • Conditioned limit theorems relating a random walk to its associate, with applications to risk reserve processes and the GI/G/1 queue
    • S. Asmussen, Conditioned limit theorems relating a random walk to its associate, with applications to risk reserve processes and the GI/G/1 queue, Adv. Appl. Probab. 14 (1982) 143-170.
    • (1982) Adv. Appl. Probab. , vol.14 , pp. 143-170
    • Asmussen, S.1
  • 3
    • 0002321011 scopus 로고
    • Approximations for the probability of ruin within finite time
    • S. Asmussen, Approximations for the probability of ruin within finite time, Scand. Act. J. (1984) 31-57; ibid. (1985) 57.
    • (1984) Scand. Act. J. , pp. 31-57
    • Asmussen, S.1
  • 4
    • 0002321011 scopus 로고
    • S. Asmussen, Approximations for the probability of ruin within finite time, Scand. Act. J. (1984) 31-57; ibid. (1985) 57.
    • (1985) Scand. Act. J. , pp. 57
  • 6
    • 0000911117 scopus 로고
    • Aspects of matrix Wiener-Hopf factorisation in applied probability
    • S. Asmussen, Aspects of matrix Wiener-Hopf factorisation in applied probability, Math. Scientist 14 (1989) 101-116.
    • (1989) Math. Scientist , vol.14 , pp. 101-116
    • Asmussen, S.1
  • 7
    • 0004147636 scopus 로고    scopus 로고
    • World Scientific Singapore, to appear
    • S. Asmussen, Ruin Probabilities (World Scientific Singapore, 1997), to appear.
    • (1997) Ruin Probabilities
    • Asmussen, S.1
  • 9
    • 21844520637 scopus 로고
    • Ruin probabilities via local adjustment coefficients
    • S. Asmussen and H.M. Nielsen, Ruin probabilities via local adjustment coefficients, J. Appl. Probab. 33 (1995) 736-755.
    • (1995) J. Appl. Probab. , vol.33 , pp. 736-755
    • Asmussen, S.1    Nielsen, H.M.2
  • 11
    • 0011631160 scopus 로고    scopus 로고
    • Convergence rates for M/G/1 queues and ruin problems with heavy tails
    • S. Asmussen and J.L. Teugels, Convergence rates for M/G/1 queues and ruin problems with heavy tails, J. Appl. Probab. 35 (1997).
    • (1997) J. Appl. Probab. , vol.35
    • Asmussen, S.1    Teugels, J.L.2
  • 12
    • 0001072998 scopus 로고
    • Residual life-time at great age
    • A.A. Balkema and L. de Haan, Residual life-time at great age, Ann. Probab. 2 (1974) 792-804.
    • (1974) Ann. Probab. , vol.2 , pp. 792-804
    • Balkema, A.A.1    De Haan, L.2
  • 13
    • 84945780730 scopus 로고
    • Saddlepoint approximations for the probability of ruin in finite time
    • O. Bardorff-Nielsen and H. Schmidli, Saddlepoint approximations for the probability of ruin in finite time, Scand. Actuarial J. (1995) 169-186.
    • (1995) Scand. Actuarial J. , pp. 169-186
    • Bardorff-Nielsen, O.1    Schmidli, H.2
  • 14
    • 38249002282 scopus 로고
    • Splitting at the infimum and excursions in half-lines for random walks and Lévy processes
    • J. Bertoin, Splitting at the infimum and excursions in half-lines for random walks and Lévy processes, Stochastic Processes Appl. 47 (1994) 17-35.
    • (1994) Stochastic Processes Appl. , vol.47 , pp. 17-35
    • Bertoin, J.1
  • 18
    • 0042034100 scopus 로고
    • On the mathematical theory of risk
    • A. Martin-Löf, ed., Stockholm. Reprinted in H. Cramér, Collected Works (Springer, Berlin)
    • H. Cramér, On the Mathematical Theory of Risk, in: A. Martin-Löf, ed., Skandia Jubilee Volume, Stockholm. Reprinted in H. Cramér, Collected Works (Springer, Berlin 1994).
    • (1994) Skandia Jubilee Volume
    • Cramér, H.1
  • 21
    • 0011631932 scopus 로고
    • A large deviation estimate for ruin probabilities
    • B. Djehiche, A large deviation estimate for ruin probabilities, Scand. Act. J. (1993) 42-59.
    • (1993) Scand. Act. J. , pp. 42-59
    • Djehiche, B.1
  • 22
    • 0001105539 scopus 로고
    • The surpluses immediately before and at ruin, and the amount of claim causing ruin
    • F. Dufresne and H.U. Gerber, The surpluses immediately before and at ruin, and the amount of claim causing ruin, Insurance: Math. Economics 7 (1988) 193-199.
    • (1988) Insurance: Math. Economics , vol.7 , pp. 193-199
    • Dufresne, F.1    Gerber, H.U.2
  • 23
    • 0001091510 scopus 로고
    • Conditioned limit theorems for random walks with negative drift
    • R. Durrett, Conditioned limit theorems for random walks with negative drift, Z. Wahrscheinlichkeitsth. Verw. Geb. 52 (1980) 277-287.
    • (1980) Z. Wahrscheinlichkeitsth. Verw. Geb. , vol.52 , pp. 277-287
    • Durrett, R.1
  • 24
    • 84971815025 scopus 로고
    • On closure and factorization properties of subexponential and related distributions
    • P. Embrechts and C.M. Goldie, On closure and factorization properties of subexponential and related distributions, J. Austral. Math. Soc. A 29 (1980) 243-256.
    • (1980) J. Austral. Math. Soc. A , vol.29 , pp. 243-256
    • Embrechts, P.1    Goldie, C.M.2
  • 25
    • 0002944036 scopus 로고
    • Estimates for the probability of ruin with special emphasis on the possibility of large claims
    • P. Embrechts and N. Veraverbeke, Estimates for the probability of ruin with special emphasis on the possibility of large claims, Insurance: Math. Economics 1 (1982) 55-72.
    • (1982) Insurance: Math. Economics , vol.1 , pp. 55-72
    • Embrechts, P.1    Veraverbeke, N.2
  • 28
    • 0001611749 scopus 로고
    • On the excursions of Markov processes in classical duality
    • P.J. Fitzsimmons, On the excursions of Markov processes in classical duality, Probab. Theory Related Fields 75 (1987) 159-178.
    • (1987) Probab. Theory Related Fields , vol.75 , pp. 159-178
    • Fitzsimmons, P.J.1
  • 30
    • 0000242401 scopus 로고
    • Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution
    • C.M. Goldie and S.I. Resnick, Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution, Adv. Appl. Probab. 20 (1988) 706-718.
    • (1988) Adv. Appl. Probab. , vol.20 , pp. 706-718
    • Goldie, C.M.1    Resnick, S.I.2
  • 32
    • 0011568124 scopus 로고
    • Excursions laws of Markov processes in classical duality
    • H. Kaspi, Excursions laws of Markov processes in classical duality, Ann. Probab. 13 (1985) 492-518.
    • (1985) Ann. Probab. , vol.13 , pp. 492-518
    • Kaspi, H.1
  • 33
    • 38249007270 scopus 로고
    • Estimation of ruin probabilities by means of hazard rates
    • C. Klüppelberg, Estimation of ruin probabilities by means of hazard rates. Insurance: Math. Economics 8 (1987) 279-285.
    • (1987) Insurance: Math. Economics , vol.8 , pp. 279-285
    • Klüppelberg, C.1
  • 34
    • 0001001934 scopus 로고
    • Subexponential distributions and integrated tails
    • C. Klüppelberg, Subexponential distributions and integrated tails, J. Appl. Probab. 25 (1988) 132-141.
    • (1988) J. Appl. Probab. , vol.25 , pp. 132-141
    • Klüppelberg, C.1
  • 35
    • 0031342881 scopus 로고    scopus 로고
    • Large deviations of heavy-tailed random sums with applications in insurance and finance
    • to appear
    • C. Klüppelberg and T. Mikosch, Large deviations of heavy-tailed random sums with applications in insurance and finance, J. Appl. Probab. 34, to appear.
    • J. Appl. Probab. , vol.34
    • Klüppelberg, C.1    Mikosch, T.2
  • 36
    • 0000733767 scopus 로고
    • Entropy estimates for ruin probabiliites
    • A. Gut and J. Holst, eds.
    • A. Martin-Löf, Entropy estimates for ruin probabiliites, in: A. Gut and J. Holst, eds., Probability and Mathematical Statistics (1983) 29-39.
    • (1983) Probability and Mathematical Statistics , pp. 29-39
    • Martin-Löf, A.1
  • 37
    • 0001021964 scopus 로고
    • Entropy, a useful concept in risk theory
    • A. Martin-Löf, Entropy, a useful concept in risk theory, Scand. Act. J. (1986) 223-235.
    • (1986) Scand. Act. J. , pp. 223-235
    • Martin-Löf, A.1
  • 39
    • 0002974752 scopus 로고
    • When does ruin occur in the collective theory of risk?
    • C.-O. Segerdahl, When does ruin occur in the collective theory of risk? Skand. Aktuar Tidsskr. (1955) 22-36.
    • (1955) Skand. Aktuar Tidsskr. , pp. 22-36
    • Segerdahl, C.-O.1
  • 40
    • 0011636533 scopus 로고
    • Moderate- and large-deviation probabilities in actuarial risk theory
    • E. Slud and C. Hoesman, Moderate- and large-deviation probabilities in actuarial risk theory, Adv. Appl. Probab. 21 (1989) 725-741.
    • (1989) Adv. Appl. Probab. , vol.21 , pp. 725-741
    • Slud, E.1    Hoesman, C.2
  • 41
    • 0002237215 scopus 로고
    • Asymptotic behaviour of Wiener-Hopf factors of a random walk
    • N. Veraverbeke, Asymptotic behaviour of Wiener-Hopf factors of a random walk, Stochastic Processes Appl. 5 (1977) 27-37.
    • (1977) Stochastic Processes Appl. , vol.5 , pp. 27-37
    • Veraverbeke, N.1


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