Explicit solution to dynamic portfolio choice problem : The continuous-time detour

TL;DR

This paper provides an explicit solution to the continuous-time dynamic portfolio choice problem with power utility, revealing how optimal stock allocation sensitivity depends on Sharpe ratio, risk aversion, and time horizon.

Contribution

It introduces an explicit solution linking continuous and discrete VAR models for portfolio sensitivity analysis, highlighting the impact of model parameters.

Findings

Optimal stock allocation is highly sensitive to Sharpe ratio.

Sensitivity increases with decreasing risk aversion.

Sensitivity grows with longer investment horizons.

Abstract

This paper solves the dynamic portfolio choice problem. Using an explicit solution with a power utility, we construct a bridge between a continuous and discrete VAR model to assess portfolio sensitivities. We find, from a well analyzed example that the optimal allocation to stocks is particularly sensitive to Sharpe ratio. Our quantitative analysis highlights that this sensitivity increases when the risk aversion decreases and/or when the time horizon increases. This finding explains the low accuracy of discrete numerical methods especially along the tails of the unconditional distribution of the state variable.