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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-diļ¬usion models where an investor has a HARA utility function, and there are potentially a large number of assets and state variables. More speciļ¬cally, 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 diļ¬erential equations to greatly facilitate economic insights and empirical applications of jump-diļ¬usion models. To examine the eļ¬ect of jump risk on investorsā behavior, we apply our results to the bond-stock mix problem and particularly revisit the bond/stock ratio puzzle in jump-diļ¬usion models. Our results cast new light on this puzzle that unlike pure-diļ¬usion models, it cannot be rationalized by the hedging demand assumption due to the presence of jumps in stock returns