擴散因子影響下的破產時間之研究
Date Issued
2003
Date
2003
Author(s)
蔡啟良
DOI
912416H002020
Abstract
In this project, we would like to consider the insurer’s surplus process of the classical
continuous time risk model containing an independent diffusion (Wiener) process.
The expectations of the present values of the time of ruin due to oscillation and a
claim, respectively, are studied. When the discount factor is set to zero, the
expectations reduce to the probabilities of the time of ruin due to oscillation and a
claim, respectively. The recursive formula and the explicit expression for the
moments (if they exist) of, and the asymptotic formula and the Tijms approximation
for, each of the expectations of the present values of the time of ruin are derived. In
addition, explicit analytical solutions to these expectations can be obtained if the
claim size distribution is an Exponential or a Gamma distribution. Finally, we will
seek for some stable and effective numerical methods for computing the expectations
of the present values of the time of ruin, and corresponding moments.
Subjects
diffusion process
time of ruin
oscillation
recursive formula
asymptotic formula
Publisher
臺北市：國立臺灣大學財務金融學系暨研究所
Type
report
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