We construct an optimal investment portfolio model with deferred annuities for an individual investor saving for retirement. The objective function consists of power utility in terms of secured retirement income from the deferred annuity purchases, as well as bequest from remaining wealth...

Using a multi-stage stochastic programming method, we suggest an optimal liability-driven investment(LDI) strategy for a closed defined-benefit pension fund including real assets. The objective is to jointly optimize contribution, funding ratio, and buyout cost, subject to a constraint on...