Lifecycle consumption-investment policies with liquid wealth constraints
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Abstract
The paper studies the life cycle optimal consumption-investment problem under a liquidity constraint (the liquid wealth process never becomes negative). For Cobb-Douglas utility, we first derive closed-form expressions for optimal consumption and investment strategy using a stopping time approach and then extend this framework to deal with the fixed leisure choice case. We also pose and solve three alternative models of optimal consumption, leisure and investment with various liquidity constraints. In addition, we obtain analytical comparative statics. We examine whether the cohort effects matter with the presence of liquidity constraints. In particular, we identify individuals who experienced low stock market returns are less willing to invest in equities and express more risk aversion. Finally, we analyze economic cost of the liquidity constraint in terms of certainty equivalent. Implications of liquidity constraints for optimal policies differ considerably from what are shown in the existing literature without liquidity constraints.