在 Erlang(2) 風險過程下貼現分配函數之研究
Date Issued
2005
Date
2005
Author(s)
蔡啟良
DOI
932416H002048
Abstract
In this project, we will try to derive explicit expressions for the discounted joint and marginal
distribution and probability density functions of the surplus immediately prior to the time of ruin
and the deficit at the time of ruin, and for the discounted distribution and probability density
function of the amount of the claim causing ruin, based on Erlang(2) assumption. Also, we will
want to show that these distribution and probability density functions satisfy defective renewal
equations. Moreover, we hope we can find the similarity between expressions for these functions
based on Erlang(1) and Erlang(2) processes, respectively. Finally, we would like to seek for some
stable and effective numerical methods of computing the expressions for the discounted
distribution and density functions, and get the numerical values for the insurer ’s and regulator ’s
information if we the claim size is exponentially distributed.
Subjects
Surplus process
Erlang(2) process
Time of ruin
Discounted distribution function
Defective renewal equation.
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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