Actuarial Studies Seminar

A closed-form solution for the continuous-time consumption model with endogenous labor income In this paper we study the consumption, labor supply, and portfolio decisions of an in nitely-lived individual who receives a wage rate and income from investment into a risky asset and a risk-free bond. Uncertainty about labor income arises endogenously, because labor supply evolves randomly over time in response to changes in nancial wealth. We derive closed-form solutions for optimal consumption, labor supply and investment strategy. We also obtain approximately log-linear relationships between optimal consumption, labor supply and retirement age, respectively. Moreover, we derive Euler equation under uncertainty of asset returns and derive a similar growth equation for expected optimal labor supply. The effects of risk-aversion coecients on optimal decisions are examined. A closed-form solution for the continuous-time consumption model with endogenous labor income Aihua Zhang