Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix

This paper studies the optimal portfolio selection problem in jump-diffusion models where an investor has a HARA utility function, and there are potentially a large number of assets and state variables. More specifically, we incorporate jumps into both stock returns and state variables, and then derive semi-analytical solutions for the optimal portfolio policy up to solving a set of ordinary differential equations to greatly facilitate economic insights and empirical applications of jump-diffusion models. To examine the effect of jump risk on investors’ behavior, we apply our results to the bond-stock mix problem and particularly revisit the bond/stock ratio puzzle in jump-diffusion models. Our results cast new light on this puzzle that unlike pure-diffusion models, it cannot be rationalized by the hedging demand assumption due to the presence of jumps in stock returns.