메뉴 건너뛰기




Volumn 27, Issue 1, 2000, Pages 19-44

The moments of the time of ruin, the surplus before ruin, and the deficit at ruin

Author keywords

Compound geometric; Deficit; Equilibrium distributions; Higher moment; Renewal equation; Surplus; Time of ruin

Indexed keywords


EID: 0001858607     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(00)00038-X     Document Type: Article
Times cited : (128)

References (32)
  • 2
    • 0034621113 scopus 로고    scopus 로고
    • Discounted probabilities and ruin theory in the compound binomial model
    • Cheng, S., Gerber, H.U., Shiu, E.S.W., 2000. Discounted probabilities and ruin theory in the compound binomial model. Insurance: Mathematics and Economics, 26, 239-250.
    • (2000) Insurance: Mathematics and Economics , vol.26 , pp. 239-250
    • Cheng, S.1    Gerber, H.U.2    Shiu, E.S.W.3
  • 3
    • 38249016441 scopus 로고
    • A remark on the moments of ruin time in classical risk theory
    • Delbaen F. A remark on the moments of ruin time in classical risk theory. Insurance: Mathematics and Economics. 9:1990;121-126.
    • (1990) Insurance: Mathematics and Economics , vol.9 , pp. 121-126
    • Delbaen, F.1
  • 7
    • 84972049017 scopus 로고
    • Recursive calculation of survival probability
    • Dickson D.C.M., Waters H.R. Recursive calculation of survival probability. ASTIN Bulletin. 21:1991;199-221.
    • (1991) ASTIN Bulletin , vol.21 , pp. 199-221
    • Dickson, D.C.M.1    Waters, H.R.2
  • 8
    • 84971892495 scopus 로고
    • The probability and severity of ruin in finite and in infinite time
    • Dickson D.C.M., Waters H.R. The probability and severity of ruin in finite and in infinite time. ASTIN Bulletin. 22:1992;177-190.
    • (1992) ASTIN Bulletin , vol.22 , pp. 177-190
    • Dickson, D.C.M.1    Waters, H.R.2
  • 9
    • 84974318058 scopus 로고
    • Some stable algorithms in ruin theory and their applications
    • Dickson D.C.M., Dos Reis A.D.E., Waters H.R. Some stable algorithms in ruin theory and their applications. ASTIN Bulletin. 25:1995;153-175.
    • (1995) ASTIN Bulletin , vol.25 , pp. 153-175
    • Dickson, D.C.M.1    Dos Reis, A.D.E.2    Waters, H.R.3
  • 11
    • 38249031188 scopus 로고
    • The probability and severity of ruin for combinations of exponential claim amount distributions and their translations
    • Dufresne F., Gerber H.U. The probability and severity of ruin for combinations of exponential claim amount distributions and their translations. Insurance: Mathematics and Economics. 7:1988;75-80.
    • (1988) Insurance: Mathematics and Economics , vol.7 , pp. 75-80
    • Dufresne, F.1    Gerber, H.U.2
  • 12
    • 21344495855 scopus 로고
    • Preservation of certain classes of life distributions under Poisson shock models
    • Fagiuoli E., Pellerey F. Preservation of certain classes of life distributions under Poisson shock models. Journal of Applied Probability. 31:1994;458-465.
    • (1994) Journal of Applied Probability , vol.31 , pp. 458-465
    • Fagiuoli, E.1    Pellerey, F.2
  • 13
  • 14
    • 84974324244 scopus 로고
    • On the probability and severity of ruin
    • Gerber H.U., Goovaerts M., Kaas R. On the probability and severity of ruin. ASTIN Bulletin. 17:1987;151-163.
    • (1987) ASTIN Bulletin , vol.17 , pp. 151-163
    • Gerber, H.U.1    Goovaerts, M.2    Kaas, R.3
  • 15
    • 0031573355 scopus 로고    scopus 로고
    • The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
    • Gerber H.U., Shiu E.S.W. The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insurance: Mathematics and Economics. 21:1997;129-137.
    • (1997) Insurance: Mathematics and Economics , vol.21 , pp. 129-137
    • Gerber, H.U.1    Shiu, E.S.W.2
  • 17
    • 0001288168 scopus 로고    scopus 로고
    • From ruin theory to pricing reset guarantees and perpetual put options
    • Gerber H.U., Shiu E.S.W. From ruin theory to pricing reset guarantees and perpetual put options. Insurance: Mathematics and Economics. 24:1999;3-14.
    • (1999) Insurance: Mathematics and Economics , vol.24 , pp. 3-14
    • Gerber, H.U.1    Shiu, E.S.W.2
  • 19
    • 0030554651 scopus 로고    scopus 로고
    • Tail of compound distributions and excess time
    • Lin X. Tail of compound distributions and excess time. Journal of Applied Probability. 33:1996;184-195.
    • (1996) Journal of Applied Probability , vol.33 , pp. 184-195
    • Lin, X.1
  • 20
    • 0001973398 scopus 로고    scopus 로고
    • Analysis of a defective renewal equation arising in ruin theory
    • Lin X., Willmot G.E. Analysis of a defective renewal equation arising in ruin theory. Insurance: Mathematics and Economics. 25:1999;63-84.
    • (1999) Insurance: Mathematics and Economics , vol.25 , pp. 63-84
    • Lin, X.1    Willmot, G.E.2
  • 22
    • 0032583017 scopus 로고    scopus 로고
    • The moments of ruin time in the classical risk model with discrete claim size distribution
    • Picard Ph., Lefevre C. The moments of ruin time in the classical risk model with discrete claim size distribution. Insurance: Mathematics and Economics. 23:1998;157-172.
    • (1998) Insurance: Mathematics and Economics , vol.23 , pp. 157-172
    • Picard, Ph.1    Lefevre, C.2
  • 23
    • 0011922394 scopus 로고    scopus 로고
    • Corrigendum to the moments of ruin time in the classical risk model with discrete claim size distribution
    • Picard Ph., Lefevre C. Corrigendum to the moments of ruin time in the classical risk model with discrete claim size distribution. Insurance: Mathematics and Economics. 25:1999;105-107.
    • (1999) Insurance: Mathematics and Economics , vol.25 , pp. 105-107
    • Picard, Ph.1    Lefevre, C.2
  • 25
    • 84903985188 scopus 로고
    • Diffusion approximations for a risk process with the possibility of borrowing and investment
    • Schmidli H. Diffusion approximations for a risk process with the possibility of borrowing and investment. Communications in Statistics, Stochastic Models. 10:1994;365-388.
    • (1994) Communications in Statistics, Stochastic Models , vol.10 , pp. 365-388
    • Schmidli, H.1
  • 26
    • 0001166636 scopus 로고    scopus 로고
    • On the distribution of the surplus prior to and at ruin
    • Schmidli H. On the distribution of the surplus prior to and at ruin. ASTIN Bulletin. 29:1999;227-244.
    • (1999) ASTIN Bulletin , vol.29 , pp. 227-244
    • Schmidli, H.1
  • 28
    • 0031998037 scopus 로고    scopus 로고
    • On a class of approximations for ruin and waiting time probabilities
    • Willmot G.E. On a class of approximations for ruin and waiting time probabilities. Operations Research Letters. 22:1997;27-32.
    • (1997) Operations Research Letters , vol.22 , pp. 27-32
    • Willmot, G.E.1
  • 29
    • 85011184651 scopus 로고    scopus 로고
    • On evaluation of the conditional distribution of the deficit at the time of ruin
    • Willmot, G.E., 2000. On evaluation of the conditional distribution of the deficit at the time of ruin. Scandinavian Actuarial Journal, 63-79.
    • (2000) Scandinavian Actuarial Journal , pp. 63-79
    • Willmot, G.E.1
  • 30
    • 0031082720 scopus 로고    scopus 로고
    • Simplified bounds on the tails of compound distributions
    • Willmot G.E., Lin X. Simplified bounds on the tails of compound distributions. Journal of Applied Probability. 34:1997;127-133.
    • (1997) Journal of Applied Probability , vol.34 , pp. 127-133
    • Willmot, G.E.1    Lin, X.2
  • 31
    • 0032585141 scopus 로고    scopus 로고
    • Exact and approximate properties of the distribution of surplus before and after ruin
    • Willmot G.E., Lin X. Exact and approximate properties of the distribution of surplus before and after ruin. Insurance: Mathematics and Economics. 23:1998;91-110.
    • (1998) Insurance: Mathematics and Economics , vol.23 , pp. 91-110
    • Willmot, G.E.1    Lin, X.2
  • 32
    • 0003706064 scopus 로고    scopus 로고
    • Lundberg approximations for compound distributions with insurance applications
    • Springer, Berlin, in press
    • Willmot, G.E., Lin, X., 2000. Lundberg approximations for compound distributions with insurance applications. Lecture Notes in Statistics. Springer, Berlin, in press.
    • (2000) Lecture Notes in Statistics
    • Willmot, G.E.1    Lin, X.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.