Multivariate stochastic loss reserving with common shock approaches

Outstanding claims liability is usually one of the largest liabilities on the balance sheet of a general insurer. Therefore, it is critical for insurers to accurately estimate their outstanding claims. Furthermore, a general insurer typically operates in multiple business lines whose risks are not perfectly dependent. This results in "diversification benefits", the consideration of which is crucial due to their effects on the aggregate reserves and capital. It is then essential to consider the dependence across business lines in the estimation of outstanding claims. The goal of this thesis is to develop new approaches to assess outstanding claims for portfolios of dependent lines. We explore the common shock technique for model developments, a very popular dependence modelling technique with distinctive strengths, such as explicit dependence structure, ease of interpretation, and parsimonious construction of correlation matrices. We also aim to enhance the practicality of our approaches by incorporating realistic and desirable model features. Motivated by the richness of the Tweedie distribution family which covers Poisson distributions, gamma distributions and many more, we introduce a common shock Tweedie framework with dependence across business lines. Desirable properties of this framework are studied, including its marginal flexibility, tractable moments, and ability to handle masses at 0. To overcome the complex distributional structure of the Tweedie framework, we formulate a Bayesian approach for model estimation and perform a real data illustration. Remarks on practical features of the framework are drawn. Loss reserving data possesses an unbalanced nature, that is, claims from different positions within and between loss triangles can vary widely as more claims typically develop in early development periods. We account for this feature explicitly in common shock models with a parsimonious common shock adjustment. Theoretical and real data illustrations are performed using the multivariate Tweedie framework. Finally, in the last part of this thesis, we develop a dynamic framework with evolutionary factors to account for claims development patterns that change over time. Calendar year dependence is introduced using common shocks. We also formulate an estimation approach that is tailored to the structure of loss reserving data and perform a real data illustration