Algorithmic Analysis of the Sparre Andersen Model in Discrete Time

Abstract

In this paper, we show that the delayed Sparre Andersen insurance risk model in discrete time can be analyzed as a doubly infinite Markov chain. We then describe how matrix analytic methods can be used to establish a computational procedure for calculating 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. Special cases of the model, namely the ordinary and stationary Sparre Andersen models, are considered in several numerical examples. KEYWORDSSparre Andersen model, discrete time, matrix analytic methods, time of ruin, surplus immediately prior to ruin, deficit at ruin.

Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends

“…In fact, similar discretization ideas (e.g., see Dickson et al [13] or Alfa and Drekic [5], pp. 306-307) can be employed to construct a discrete-time approximation to a continuous-time analogue of our proposed risk model.…”

“…In particular, Drekic and Mera [4] considered the ruin analysis of a threshold-based dividend payment strategy in a discrete-time Sparre Andersen model. Their analysis was an extension of the work by Alfa and Drekic [5], in which a Sparre Andersen insurance risk model in discrete time was analyzed as a doubly-infinite Markov chain to establish a computational procedure for calculating the joint probability distribution of the time of ruin, the surplus immediately prior to ruin, and the deficit at ruin.…”