Analysis of a Threshold Strategy in a Discrete-time Sparre Andersen Model

Actuarial Science

Mera, Ana Maria

University of Waterloo

关键词: Actuarial Science;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3323/1/ThesisFinal.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis, it is shown that the application of a threshold on thesurplus level of a particular discrete-time delayed Sparre Anderseninsurance risk model results in a process that can be analyzed as adoubly infinite Markov chain with finite blocks.Two fundamental cases,encompassing all possible values of the surplus level at the time of the first claim, are explored in detail.Matrix analytic methods are employed to establish a computational algorithm for each case. The resulting procedures are then used to calculate the probabilitydistributions associated with fundamental ruin-related quantities ofinterest, such as the time of ruin, the surplus immediately prior toruin, and the deficit at ruin.The ordinary Sparre Andersen model, animportant special case of the general model, with varying threshold levels isconsidered in a numerical illustration.