Valuation of Hybrid Financial and Actuarial Risks

How to valuate future cash flows is a fundamental problem in both finance and actuarial science. (Pricing of financial products, premium and technical provisions of insurance contracts). However, traditional ways of valuing actuarial or financial liabilities are quite different. In Finance, the pricing is based on risk neutral expectations of discounted cash flows, originally justified by hedging portfolios. In Insurance, premium calculation principles use a real world best estimate value plus a risk premium, given for instance by a standard deviation approach and justified by pooling effect of independent contracts. This dichotomy of paradigm is debatable and could encourage us to find a unifying tool. This also becomes a real challenge when it comes to pricing for instance hybrid life insurance or pension products mixing actuarial and financial risks. Different techniques have been recently developed in the actuarial literature in order to address this fundamental valuation problem in a harmonious manner, in order to remain simultaneously market consistent and actuarial consistent. Another issue when pricing insurance risks is the presence of diversifiable and systematic risks requiring also different risk measurement. Finally, when the valuation has to be dynamic (for instance technical provisions), the time consistency of the method is an additional difficulty.