Portfolio Choice and Fair Pricing in Life and Pension Insurance

We investigate the implications of optimal portfolio choice on fair pricing of specific pension insurance contracts. We motivate that the manager of the insurance company should optimize utility of final payout for the policy holders. The payout to the policy holder is highly non-linear in wealth, implying that the optimization problem is non-trivial. Still, we find closed form solutions. Simultaneously with the optimal portfolio choice we find fair contract specifications in the sense that the market values of future claims to policy and equity holders, respectively, are equal to their initial deposits. We find that the introduction of a dynamic optimal portfolio changes the fair contract specifications as well as the comparative statics considerably compared to the case with a fixed underlying portfolio. The utility loss, measured by a certainty equivalent wealth, of not introducing portfolio choice can have an arbitrary sign since the fair contract specifications change by the introduction of optimal portfolio choice. Our findings illustrate that dynamic portfolio choice should not be ignored when analyzing fair insurance contracts. JEL Classification: G11, G13, G22