City Research Online

Abstract

The work presented in this dissertation is motivated by the observation that the classical (re)insurance risk modelling assumptions of independent and identically distributed claim amounts, Poisson claim arrivals and premium income accumulating linearly at a certain rate, starting from possibly non-zero initial capital, are often not realistic and violated in practice. There is an abundance of examples in which dependence is observed at various levels of the underlying risk model. Developing risk models which are more general than the classical one and can successfully incorporate dependence between claim amounts, consecutively arriving at the insurance company, and/or dependence between the claim inter-arrival times, is at the heart of this dissertation. The main objective is to consider such general models and to address the problem of (non-) ruin within a finite-time horizon of an insurance company. Furthermore, the aim is to consider general risk and performance measures in the context of a risk sharing arrangement such as an excess of loss (XL) re insurance contract. There are two parties involved in an XL re insurance contract and their interests are contradictory, as has been first noted by Karl Borch in the 1960s. Therefore, we define joint, between the cedent and the reinsurer, risk and performance measures, both based on the probability of ruin, and show how the latter can be used to optimally set the parameters of an XL reinsurance treaty. Explicit expressions for the proposed risk and performance measures are derived and are used efficiently in numerical illustrations.

Publication Type:	Thesis (Doctoral)
Departments:	Bayes Business School > Actuarial Science & Insurance Doctoral Theses Bayes Business School > Bayes Business School Doctoral Theses

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