Abstract
This paper provides a novel five-component decomposition of optimal dynamic portfolio choice. It reveals the simultaneous impacts from market incompleteness and wealth-dependent utilities. The decomposition leads to implementation via either closed-form solutions or Monte Carlo simulations. With a nonrandom but time-varying interest rate, we can explicitly solve for the optimal policy under the wealth-dependent HARA utility. It is a combination of a bond holding scheme and the corresponding simpler CRRA strategy. Under incomplete markets with a stochastic volatility model estimated on US equity data, wealth-dependence introduces sophisticated cycle-dependence for optimal policy and hysteresis effect in Sharpe ratio.
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