Modeling with the Multivariate Probabilistic Trend Family

This paper motivates the benefits of modeling trends, volatility and correlations through a study of real data triangles. We show that a model that is demonstrably unable to forecast the recent past of the historical triangle cannot be expected to tell us anything useful about the future of the same process. Naturally, the same basic model fitted by applying a more sophisticated tool will suffer the same fate. The use of GLMs, bootstrapping, or Bayesian statistics cannot avoid the basic defects of traditional methods. With traditional techniques the parameters (e.g. age-to-age factors) are a function of the data. By contrast, in the Probabilistic Trend Family (PTF) modeling framework the model design as well as the parameters are a function of the data. We illustrate PTF modeling (e.g., Barnett and Zehnwirth, 2000) on a variety of real triangles. The PTF modeling framework is extended to the simultaneous modeling of multiple triangles. The multivariate modeling framework (MPTF), apart from describing the volatility in each triangle also describes correlations between them in two different ways. The MPTF modeling framework can be used in a number of innovative ways yielding useful information about the risk characteristics of the business. There are important implications for economic capital calculations and optimal retention. In order to compute economic capital for reserve risk and underwriting risk the correlations between lines of business need to be known. To assess the correlations accurately (whether from related trends or correlated errors), a model for each line that describes the trend structure and the volatility about the trend structure needs first to be identified.