Decomposition of Optimal Portfolio Weight in a Jump-Diffusion Model and Its Applications

Abstract

This article solves the portfolio choice problem in a multi-asset jump-diffusion model. We decompose the optimal portfolio weight into components that correspond to a collection of fictitious economies, one of which is a standard diffusion economy, and the others of which are pure-jump economies. We derive a semi-closed-form solution for the optimal portfolio weight, and investigate its properties with or without ambiguity aversion. We find that an investor may not reduce her investment in risky assets when facing more frequent jumps, as suggested by a single-asset jump-diffusion model. Moreover, an investor who is extremely cautious about her estimates of higher moments of asset returns may still hold risky assets, contrary to the prediction of a pure-diffusion model with ambiguity aversion to the first moment. (JEL G11) It has been widely documented that stock returns exhibit both stochastic volatility and jumps (see, for example, Bakshi, Cao, and Chen 1997; Bates 2000; Eraker, Johannes, and Polson 2003). With jumps, an asset return model can explicitly allow for sudden but infrequent market movements of large magnitude, thus capturing both the “skewed ” and “fat-tailed ” features of stock

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