Rank-Based Multivariate Sarmanov for Modeling Dependence Between Loss Reserves

Abstract

The dependence between multiple lines of business has an important impact on determining loss reserves and risk capital, which are crucial elements of risk management for an insurance portfolio. In this work, we show that the Sarmanov family of multivariate distribution can be used for dependent lines of business using a rank-based method estimation. In fact, an inadequate choice of the dependence structure may negatively impact the estimation of the marginals, which might lead to an undesirable effect on reserve computation. Thus, we propose a two-stage inference strategy in this thesis. We show that this strategy leads to robust estimation and better capture the dependence between the risks. We also show that it leads to smaller risk capital and a better diversification benefit.

We introduce the two-stage inference using the Sarmanov distribution. First, we fit the marginals with generalized linear models (GLMs) and obtain the corresponding residuals. Secondly, the Sarmanov family of bivariate distributions links these marginals through the rank of residuals. We also show that this can be extended to a multivariate case.

To illustrate this method, we analyzed two sets of data. For the bivariate case, we considered an insurance portfolio consisting of personal and commercial auto lines provided by a major US property-casualty insurer. We also used the data from three lines of business of a large Canadian insurance company for the multivariate dependence case.