This paper establishes a new decomposition of optimal dynamic portfolio choice under general incomplete-market diffusion models by disentangling the fundamental impacts on optimal policy from market incompleteness and flexible wealth-dependent utilities. We derive explicit dynamics of the components for the optimal policy, and obtain an equation system for solving the shadow price of market incompleteness, which is found to be dependent on both market state and wealth level. We identify a new important hedge component for non-myopic investors to hedge the uncertainty in shadow price due to variation in wealth level. As an application, we establish and compare the decompositions of optimal policy under general models with the prevalent HARA and CRRA utilities. Under nonrandom but possibly time-varying interest rate, we solve in closed-form the HARA policy as a combination of a bond holding scheme and a corresponding CRRA strategy. Finally, we develop a simulation method to implement the decomposition of optimal policy under the general incomplete market setting, whereas existing approaches remain elusive .
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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under general incomplete-market diffusion models by disentangling the fundamental impacts on optimal policy
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We derive explicit dynamics of the components for the optimal policy, and obtain an equation system for solving the shadow price of market incompleteness, which is found to be dependent on both market state and wealth level. We identify a new important hedge component for non-myopic investors to hedge the uncertainty in shadow price due to variation in wealth level. As an application, we establish and compare the decompositions of optimal policy under general models with the prevalent HARA and CRRA utilities. Under nonrandom but possibly
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solve in closed-form the HARA policy as
can explicitly solve for the optimal policy under the wealth-dependent HARA utility. It is
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Finally, we develop a simulation method to implement the decomposition of optimal policy under the general incomplete market setting, whereas existing approaches remain elusive
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