Analysis of a Threshold Strategy in a Discrete-time Sparre Andersen Model
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Date
2007-09-26T19:17:14Z
Authors
Mera, Ana Maria
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
In this thesis, it is shown that the application of a threshold on the
surplus level of a particular discrete-time delayed Sparre Andersen
insurance risk model results in a process that can be analyzed as a
doubly 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 probability
distributions associated with fundamental ruin-related quantities of
interest, such as the time of ruin, the surplus immediately prior to
ruin, and the deficit at ruin. The ordinary Sparre Andersen model, an
important special case of the general model, with varying threshold
levels is
considered in a numerical illustration.