In the aftermath of the 2007-2008 fi nancial crisis, there has been criticism of mathematics and the mathematical models used by the fi nance industry. We answer these criticisms through a discussion of some of the actuarial models used in the pricing of credit derivatives. As an example, we focus in particular on the Gaussian copula model and its drawbacks. To put this discussion into its proper context, we give a synopsis of the fi nancial crisis and a brief introduction to some of the common credit derivatives and highlight the diffi culties in valuing some of them.We also take a closer look at the risk management issues in part of the insurance industry that came to light during the fi nancial crisis. As a backdrop to this, we recount the events that took place at American International Group during the fi nancial crisis. Finally, through our paper we hope to bring to the attention of a broad actuarial readership some "lessons (to be) learned" or "events not to be forgotten".
Various types of structures that enable a group of individuals to pool their mortality risk have been proposed in the literature. Collectively, the structures are called pooled annuity funds. Since the pooled annuity funds propose different methods of pooling mortality risk, we investigate the connections between them and find that they are genuinely different for a finite heterogeneous membership profile.We discuss the importance of actuarial fairness, defined as the expected benefits equalling the contributions for each member, in the context of pooling mortality risk and comment on whether actuarial unfairness can be seen as solidarity between members. We show that, with a finite number of members in the fund, the group self-annuitization scheme is not actuarially fair: some members subsidize the other members. The implication is that the members who are subsidizing the others may obtain a higher expected benefit by joining a fund with a more favourable membership profile. However, we find that the subsidies are financially significant only for very small or highly heterogeneous membership profiles.
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