This paper studies the optimal post-retirement allocation of wealth between financial investments and life annuities within an Equity-Linked Annuity Defined Contribution (ELA-DC) scheme. We extend the standard framework by allowing partial annuitisation, thereby incorporating bequest motives into the retirement decision. The resulting continuous-time stochastic control problem jointly determines the optimal investment and annuitisation strategies in a setting with stochastic interest rates, equity returns, mortality, and dependence among these risk factors. The problem is solved numerically using a Least-Squares Monte Carlo approach, which is able to handle the high-dimensional state space and the dynamic optimisation problem. Numerical results show that the optimal strategies are highly sensitive to individuals’ risk aversion, bequest preferences, and the mandatory annuitisation age. In particular, greater risk aversion leads to more conservative portfolios and smoother annuitisation paths, while a later compulsory annuitisation age supports higher equity exposure and delays the conversion of wealth into lifetime income. These findings provide insights for the design of post-retirement defined contribution products that better balance investment performance, longevity protection, and bequest objectives.
The stochastic comparison of random cash flows when rates of interest are random and non-negative is approached in this manuscript. Some comparison criteria are considered for that purpose. Namely, those comparisons are performed in terms of random vectors of present values of future cash flows at different times, by means of internal rates of return of cash flows with an initial outflow, and in terms of the corresponding present values of cash flows at start times. Sufficient conditions to make comparisons with the above criteria are developed. The results are illustrated with applications and examples involving some probabilistic models of cash flows and rates of interest.
