An importance sampling algorithm for estimating extremes of perpetuity sequences
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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An importance sampling algorithm for estimating extremes of perpetuity sequences. / Collamore, Jeffrey F.
AIP Conference Proceedings. Bind 1479 American Institute of Physics, 2012. s. 1966-1969.Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - An importance sampling algorithm for estimating extremes of perpetuity sequences
AU - Collamore, Jeffrey F.
N1 - NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. - 19–25 September 2012, Kos, Greece
PY - 2012
Y1 - 2012
N2 - In a wide class of problems in insurance and financial mathematics, it is of interest to study the extremal events of a perpetuity sequence.This paper addresses the problem of numerically evaluating these rare event probabilities. Specifically, an importance sampling algorithm is described whichis efficient in the sense that it exhibits bounded relative error, and which is optimal in an appropriate asymptotic sense. Themain idea of the algorithm is to use a ``dual"change of measure, which is employed to an associated Markov chain over a randomly-stopped time interval.The algorithm also makes use of the so-called forward sequences generated to the given stochastic recursion,together with elements of Markov chain theory.
AB - In a wide class of problems in insurance and financial mathematics, it is of interest to study the extremal events of a perpetuity sequence.This paper addresses the problem of numerically evaluating these rare event probabilities. Specifically, an importance sampling algorithm is described whichis efficient in the sense that it exhibits bounded relative error, and which is optimal in an appropriate asymptotic sense. Themain idea of the algorithm is to use a ``dual"change of measure, which is employed to an associated Markov chain over a randomly-stopped time interval.The algorithm also makes use of the so-called forward sequences generated to the given stochastic recursion,together with elements of Markov chain theory.
U2 - 10.1063/1.4756571
DO - 10.1063/1.4756571
M3 - Article in proceedings
SN - 8-0-7354-1091-6
VL - 1479
SP - 1966
EP - 1969
BT - AIP Conference Proceedings
PB - American Institute of Physics
ER -
ID: 45682569