Household consumption, investment and life insurance

A combined stochastic programming and optimal control approach to personal finance and pensions

“…The research to date has tended to focus on deriving the explicit solution for the controls over the same period; either until retirement, see e.g. Cairns et al (2006) and Bruhn and Steffensen (2011), after retirement, see e.g. Gerrard et al (2004Gerrard et al ( , 2006 and He and Liang (2013), or generally over the life cycle, see e.g.…”

“…The problem is solved first for the period after retirement, where we refer to Bruhn and Steffensen (2011), and then for the period before retirement, which is control model Table 2: Problem (B) before and after retirement. Explicit solution and MSP solution with various modifications for the expected value of the savings and optimal benefits (in 1000 EUR), and optimal investment in both risky assets and in the first risky asset (π * t = π * 1 t + π * 2 t ).…”

“…Probably the most influential papers in this field have been written by Merton (1969Merton ( , 1971 who defined the original problem of optimizing utility of consumption and terminal wealth over a fixed time horizon for an investor. This work has inspired many researchers who either expanded the original model or investigated different objective functions, by introducing for instance the lifetime uncertainty, sum insured and the labor income, Richard (1975), stochastic interest rate, Munk and Sørensen (2004), salary uncertainty, Cairns et al (2006), multiperson household, Bruhn and Steffensen (2011), borrowing constraints, Byung and Yong (2011), or constant linear taxation, Bruhn (2013). Applications within defined contribution pension scheme with a focus on the investment strategy either during the accumulation or post retirement phase (decumulation) together with the optimal time of annuitization, have been considered by Milevsky and Young (2007) and Gerrard et al (2004Gerrard et al ( , 2012.…”

“…The problem of optimizing expected utility of consumption after retirement in the case where the person controls investment π * t , life insurance I * t , and consumption c * t , and has no bequest motive, has been solved in Bruhn and Steffensen (2011). The authors derive the optimal value function…”

Optimal retirement planning with a focus on single and joint life annuities

“…If the objective is to bequeath to one of the spouses, the couple chooses positive k (x) and/or k (y) , corresponding to the bequest for the wife (x) and/or the husband (y). Thus, we extend the objective suggested in Bruhn and Steffensen (2011), and introduce the following objective function…”