Approximating the Finite-Time Ruin Probability under Interest Force

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Abstract

We present an algorithm to determine both a lower and an upper bound for the finite-time probability of ruin for a risk process with constant interest force. We split the time horizon into smaller intervals of equal length and consider the probability of ruin in case premium income for a time interval is received at the beginning (resp. end) of that interval, which yields a lower (resp. upper) bound.For both bounds we present a renewal equation which depends on the distribution of the present value of the aggregate claim amount in a time interval.This distribution is determined through a generalization of Panjer's (1981) recursive method.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages18
Volume2000-111
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper
Volume2000-111

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Finite-time Ruin Probability
Probability of Ruin
Interval
Renewal Equation
Upper bound
Risk Process
Recursive Method
Horizon

Keywords

  • interest rate
  • probability

Cite this

Brekelmans, R. C. M., & De Waegenaere, A. M. B. (2000). Approximating the Finite-Time Ruin Probability under Interest Force. (CentER Discussion Paper; Vol. 2000-111). Tilburg: Operations research.
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Brekelmans, RCM & De Waegenaere, AMB 2000 'Approximating the Finite-Time Ruin Probability under Interest Force' CentER Discussion Paper, vol. 2000-111, Operations research, Tilburg.

Approximating the Finite-Time Ruin Probability under Interest Force. / Brekelmans, R.C.M.; De Waegenaere, A.M.B.

Tilburg : Operations research, 2000. (CentER Discussion Paper; Vol. 2000-111).

Research output: Working paperDiscussion paperOther research output

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T1 - Approximating the Finite-Time Ruin Probability under Interest Force

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Y1 - 2000

N2 - We present an algorithm to determine both a lower and an upper bound for the finite-time probability of ruin for a risk process with constant interest force. We split the time horizon into smaller intervals of equal length and consider the probability of ruin in case premium income for a time interval is received at the beginning (resp. end) of that interval, which yields a lower (resp. upper) bound.For both bounds we present a renewal equation which depends on the distribution of the present value of the aggregate claim amount in a time interval.This distribution is determined through a generalization of Panjer's (1981) recursive method.

AB - We present an algorithm to determine both a lower and an upper bound for the finite-time probability of ruin for a risk process with constant interest force. We split the time horizon into smaller intervals of equal length and consider the probability of ruin in case premium income for a time interval is received at the beginning (resp. end) of that interval, which yields a lower (resp. upper) bound.For both bounds we present a renewal equation which depends on the distribution of the present value of the aggregate claim amount in a time interval.This distribution is determined through a generalization of Panjer's (1981) recursive method.

KW - interest rate

KW - probability

M3 - Discussion paper

VL - 2000-111

T3 - CentER Discussion Paper

BT - Approximating the Finite-Time Ruin Probability under Interest Force

PB - Operations research

CY - Tilburg

ER -