Dynamic Asset Allocation with Stochastic Income and Interest Rates

We investigate the optimal investment and consumption choice of individual investors with uncertain future labor income operating in a financial market with stochastic interest rates. Since the present value of the individual's future income is a main determinant of the optimal behavior and this present value depends heavily on the interest rate dynamics, the joint stochastics of income and interest rates will have consequences beyond the separate effects of stochastic income and stochastic interest rates. We study both the case where income risk is spanned and there are no portfolio constraints and the case with non-spanned income risk and a constraint ruling out borrowing against future income. For the spanned, unconstrained problem we study a special case in which we obtain closed-form expressions for the optimal policies. For the unspanned, constrained problem we implement a numerical solution technique and compare the solutions to the spanned, unconstrained problem. We also allow for typical life-cycle variations in labor income.