Asset Allocation and Optimal Retirement with Sticky Wages: a Stochastic Optimal Control Problem with Delay

Cecilia Prosdocimi^*

We consider a stochastic optimal control problem with state constraint, where the state is driven by a dynamic with delay. We thus naturally embed the problem in an infinite dimensional space. We face this issue studying the consumption-investment plan over all her life (life-cycle model) of an agent who optimally allocates her wealth to different investment opportunities, subject to borrowing constraints. The agent receives sticky wages, i.e. her labour income depends by the past of the financial market. We solve for the optimal asset allocation before and after retirement. We use our results to provide insights into the impact of wage rigidity and endogenous retirement on life-cycle asset allocation decisions.

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Minisymposion: On Optimal Feedback Control for Partial Differential Equations: Theory and Numerical Methods