In this paper, we introduce the 3-step hedge-based valuation for the valuation of hybrid claims. We consider an insurance portfolio which is exposed to traded risks, diversifiable risks and non-traded systematic risks. The class of 3-step hedge-based valuations is equivalent with the class of fair valuations. Closed-form solutions are derived for a portfolio of unit-linked contracts under the assumption of independence between financial and non-financial risks. We also consider the additive 3-step valuation and show that this additive valuation is a member of the more general class of 3-step hedge-based valuations.

In this paper, a discrete-time framework is proposed to value power exchange options with counterparty default risk, where counterparty risk is considered in a reduced-form setting and the variance processes of the underlying assets are captured by GARCH processes. In addition, the proposed model allows for the correlation between the intensity of default and the variances of the underlying assets by breaking down the total risk into systematic and idiosyncratic components. By dint of measure-change techniques and characteristic functions, we obtain the closed-form pricing formula for the value of power exchange options with counterparty default risk. Finally, numerical results are presented to show the power exchange option values.

A major outcome of ERM activities in insurance companies has been the bringing together of all of the key risks in the company, to be managed collectively in a holistic fashion. The authors of this paper believe that an ERM framework also needs to look beyond the company, and have regard to the risk management needs of investors, from the point of view of the contribution of the insurance company to the overall risk and reward of their total investment portfolios. To meet these needs, the ERM framework needs to provide sufficient information on topics such as systematic risk, potential correlations of earnings from future new business with macroeconomic trends, other risks to franchise value, and sources of model risk within the company. The paper does not provide solutions for the issues described above; but limits itself to describing and discussing the direction for some important new initiatives in ERM activities.

This paper shows how the powerful and flexible tool of stochastic modelling can be applied to a range of business decisions extending far beyond the asset allocation solutions that are common to many asset/liability modelling studies. The example used to demonstrate these techniques is a general insurance case study, but similar principles can be extended to many different business situations. At each stage of the analysis we consider the implications of modern financial theory on the management decision process together with a practical perspective on observed behaviour in the real world. Opportunities are taken to suggest directions in which further research may be of benefit to the actuarial profession.