Details
| Original language | English |
|---|---|
| Pages (from-to) | 802-827 |
| Number of pages | 26 |
| Journal | Advances in applied probability |
| Volume | 28 |
| Issue number | 3 |
| Publication status | Published - Sept 1996 |
Abstract
Let ψ(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ψ(u) behaves asymptotically like a multiple of exp (-Ru) where R is the adjustment coefficient; R depends on the premium income rate, the claim size distribution and the distribution of the time between claim arrivals. Estimation of R has been considered by many authors. In the present paper we deal with confidence bounds for R. A variety of methods is used, including jackknife estimation of asymptotic variances and the bootstrap. We show that, under certain assumptions, these procedures result in interval estimates that have asymptotically the correct coverage probabilities. We also give the results of a simulation study that compares the different techniques in some particular cases.
Keywords
- Adjustment coefficient, Bootstrap, Jackknife: bias correction, Nonparametric estimation, Random walk, Risk theory, Ruin probability
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Applied Mathematics
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In: Advances in applied probability, Vol. 28, No. 3, 09.1996, p. 802-827.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Confidence bounds for the adjustment coefficient
AU - Pitts, Susan M.
AU - Grübel, Rudolf
AU - Embrechts, Paul
PY - 1996/9
Y1 - 1996/9
N2 - Let ψ(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ψ(u) behaves asymptotically like a multiple of exp (-Ru) where R is the adjustment coefficient; R depends on the premium income rate, the claim size distribution and the distribution of the time between claim arrivals. Estimation of R has been considered by many authors. In the present paper we deal with confidence bounds for R. A variety of methods is used, including jackknife estimation of asymptotic variances and the bootstrap. We show that, under certain assumptions, these procedures result in interval estimates that have asymptotically the correct coverage probabilities. We also give the results of a simulation study that compares the different techniques in some particular cases.
AB - Let ψ(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ψ(u) behaves asymptotically like a multiple of exp (-Ru) where R is the adjustment coefficient; R depends on the premium income rate, the claim size distribution and the distribution of the time between claim arrivals. Estimation of R has been considered by many authors. In the present paper we deal with confidence bounds for R. A variety of methods is used, including jackknife estimation of asymptotic variances and the bootstrap. We show that, under certain assumptions, these procedures result in interval estimates that have asymptotically the correct coverage probabilities. We also give the results of a simulation study that compares the different techniques in some particular cases.
KW - Adjustment coefficient
KW - Bootstrap
KW - Jackknife: bias correction
KW - Nonparametric estimation
KW - Random walk
KW - Risk theory
KW - Ruin probability
UR - http://www.scopus.com/inward/record.url?scp=0001441869&partnerID=8YFLogxK
U2 - 10.1017/S0001867800046504
DO - 10.1017/S0001867800046504
M3 - Article
AN - SCOPUS:0001441869
VL - 28
SP - 802
EP - 827
JO - Advances in applied probability
JF - Advances in applied probability
SN - 0001-8678
IS - 3
ER -