The impact of liquidity constraints and cashflows on the optimal retirement problem

In this work we analytically solve an optimal retirement problem, in which the agent optimally allocates consumption, leisure rate and invests in a risk-free and risky asset to maximize a gain function characterized by a power utility function of consumption and leisure, through the duality method. The model is general enough to be compatible with both lifetime debt repayments and pension plans. We impose different liquidity constraints and cashflows over different time spans and conduct a sensitivity analysis to discover the effect of this kind of constraint. We show that pre- and post-retirement constraints have opposite effects on optimal wealth threshold of retirement. Moreover, pre-retirement constraints do not impact on post-retirement control strategies, while the opposite does not hold true.