Optimal pension insurance design

In this paper we analyze how the traditional life and pension contracts with a guaranteed rate of return can be optimized to increase customers’ welfare. Given that the contracts have to be priced correctly, we use individuals’ preferences to find the preferred design. Assuming CRRA utility, we cannot explain the existence of any form of guarantees. Through numerical solutions we quantify the difference (measured in certainty equivalents) to the preferred Merton solution of direct investments in a fixed proportion of risky and risk free assets. The largest welfare loss seems to come from the fact that guarantees are effective by the end of each year, not only by the expiry of the contract. However, the demand for products with guarantees may be explained through behavioral models. We use cumulative prospect theory as an example, showing that the optimal design is a simple contract with a life-time guarantee and no default option.     

Intergenerational Effects of Guaranteed Pension Contracts

In this paper we show that there exist intergenerational cross-subsidization effects in guaranteed interest rate life and pension contracts as the different generations partially share the same reserves. Early generations build up bonus reserves, which are left with the company at expiry of the contract. These bonus reserves function partly as a subsidy of later generations, such that the latter earn a risk-adjusted return above the risk-free rate. Furthermore, we show that this subsidy may be large enough to explain why late generations buy guaranteed interest rate products, which otherwise would not have been part of the optimal portfolio allocation.