Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework

A regular equilibrium solves the extended HJB system

“…Early papers in mathematical finance to study the game-theoretic approach to time-inconsistent problems are [2,15,16,17] where PDE methods for specific time-inconsistent problems -that are similar to the general method relying on the extended HJB system of [6,7] -are developed. Recent publications that use different versions of the extended HJB system to study time-inconsistent stochastic control problems include [4,8,9,19,23,25,26,27,35]. In [14], the equilibrium of a time-inconsistent control problem is characterized by a stochastic maximum principle.…”

“…The pre-commitment approach is in this example to maximize (19) over admissible controls, by treating x as an arbitrary but fixed parameter. It is easy to see that the pre-commitment optimal control is, for any fixed x,…”

Optimal Investment Policy in a Pension Fund System with Return Clause and Multiple Assets under Volatility Risks

“…[14], studied the general theory of Markovian time inconsistent stochastic control problems. Recently, the study of optimal investment policy with return of contributions clause has taken a centre stage since members of the scheme are faced with mortality risk; these include [15], who investigated optimal investment strategy for a defined contribution pension scheme with the return of premiums clauses in a mean-variance utility function. [16], Investigated equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under constant elasticity of variance model.…”

Equilibrium investment strategy for defined-contribution pension schemes with generalized mean–variance criterion and mortality risk

“…Nkeki (2013) studies a mean-variance DC pension management problem with time-dependent salary, and compares the optimal portfolios under quadratic utility function, power utility function and exponential utility function. He and Liang (2013) introduce the return of premium clauses into the portfolio model with the mean-variance criterion for a DC pension plan during the accumulation phase, and derive a time-consistent investment strategy within the game theoretic framework. Menoncin and Vigna (2013) consider a mean-variance investment problem for a DC pension plan with a stochastic interest rate in the accumulation phase.…”

“…However, in the above-mentioned literature, except for He and Liang (2013), the optimal investment strategy with the mean-variance criterion is time-inconsistent, which is only optimal at the initial time. That is, the optimal strategy at time m does not agree with that at time n, where n > m, because the meanvariance criterion does not have the iterated expected property.…”