1 Department of Management Engineering, Technical University of Denmark2 Management Science, Department of Management Engineering, Technical University of Denmark3 Princeton University
The paper develops a pension product that can be oered in a dened contribution pension scheme as a deferred or immediate life annuity. The product is characterized by linking an individual's savings directly to market returns and differs from the products available in the market by being adjusted to individual needs. We argue that the asset allocation, the payout prole and the insured sum should not only depend on the plan member's age (or time left to retirement), nor only on her risk preferences, but should capture personal and economical characteristics. Among other factors, we include current wealth, expected lifetime salary progression, mandatory and voluntary pension contributions, expected state retirement pension, choice of assets, subjective lifetime expectancy and bequest motive. Specically, the asset allocation strategy, the payout prole and the level of insured sum dening the new product are optimal under the expected utility function of retirement benets given the individual's characteristics. The problem is solved via a model that combines two optimization approaches: stochastic optimal control and multistage stochastic programming. The rst method is common in nancial and actuarial literature, but results in theoretical values. However, the latter, which is characteristic for operations research, has highly practical application. We present the operations research methods with application of immediate and deferred life annuities in the Danish market, which have potential to stimulate new thinking and add to actuarial practice.