Effect of lifetime uncertainty on consumption/investment with luxury bequest motives

We study optimal consumption/investment of a retiree who has luxury bequest motives and faces the nonnegative bequest constraint. His lifetime is uncertain but actuarially fair life insurance-annuity policies are available. We obtain a closed form solution by using a dynamic programming method, and investigate the effects of lifetime uncertainty and the presence of life insurance-annuity on the consumption/investment policies.