On the decomposition of risk in life insurance

Assuming a product space model for biometric and financial events, there exists a rather natural principle for the decomposition of gains of life insurance contracts into a financial and a biometric part using orthogonal projections. In a discrete time framework, the paper shows the connection between this decomposition, locally variance-optimal hedging and the so-called pooling of biometric risk contributions. For example, the mean aggregated discounted biometric risk contribution per client converges to zero almost surely for an increasing number of clients. A general solution of Bühlmann’s AFIR-problem is proposed. JEL: G10, G13, G22 MSC: 91B24, 91B28, 91B30