Price Optimisation and Statistical Modeling of Dependent Risks

The key objectives of insurance companies on a yearly basis are two-fold. First, given the high competition in the insurance market, insurers compete intensively on price, quality of service, financial strength and many other factors across every lines of business. However, they are mainly concerned in increasing their profit, generate more sales and retain existing customers at the end of the calendar year in order to stand out from their competitors. In this respect, a new and evolving concept has recently been introduced in the scope of insurance; Price Optimisation. It is referred to the practice of increasing or decreasing premium rates of policyholders based on non-related risk factors. In this thesis, we show that the optimisation problems rely on an appropriate modeling of the elasticity of the customer due to premium change for the cases of new and renewal business. Secondly, nowadays, insurance companies are governed by new regulations requiring them to hold a certain amount of capital, usually known as the Economic Capital, to cover their unexpected losses. The calculation of this capital falls under the Solvency II in Europe or the Swiss Solvency Test (SST) in Switzerland, for instance, and is based on an appropriate modeling of the dependence structure between insurance risks. This dependency is described by means of a copula. Therefore, in this thesis, we shall present applications of the copula approach in several insurance areas, namely in the computation of reinsurance premiums (Stop-Loss and Excess-of-Loss), risk aggregation and capital allocation when considering dependency between claims sizes and/or number of claims for two or more insurance portfolios as well as the fit of a copula model to some concrete insurance dataset. In this thesis, we shall explore both objectives in details