Modelling Quantile Premium for Dependent LOBs in Property/Casualty Insurance
An essential element of an insurance company activity is the calculation of what is referred to as the pure premium for a single risk, defined as the mean of total claim amount. The additional information is to look for the VaR risk measure or quantile premium. It is an easy task in case of only one line of business (LOB) covered by the premium. Nowadays the typical situation is to cover several LOBs in one risk, as e.g. automobile risk can be split into TPL (third part liability), MOD (motor own damage), fire, theft and so on. In this case, quantile premium, which captures the dependency among LOBs, can improve in practice the determination of risk-based capital requirements for P&C insurers, setting overall risk target by senior management, pricing of excess-of-loss reinsurance treaties or designing scenario analyses, to name a couple of applications. The goal of this paper is to put forward copula-based regression model dedicated to estimate the quantile premium for single risk in insurance covering dependent LOBs. To obtain the premium, first the dependency between LOBs is captured by the copula and second the Monte Carlo simulation is performed. Finally, some properties of quantile premium are analyzed. All computations are carried out with R program and the R code is available to download (see https://woali.github.io/rphdstatistics/).
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