Annals of Applied Probability

Portfolio choice with jumps: A closed-form solution

Yacine Aït-Sahalia, Julio Cacho-Diaz, and T. R. Hurd

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We analyze the consumption-portfolio selection problem of an investor facing both Brownian and jump risks. We bring new tools, in the form of orthogonal decompositions, to bear on the problem in order to determine the optimal portfolio in closed form. We show that the optimal policy is for the investor to focus on controlling his exposure to the jump risk, while exploiting differences in the Brownian risk of the asset returns that lies in the orthogonal space.

Article information

Ann. Appl. Probab., Volume 19, Number 2 (2009), 556-584.

First available in Project Euclid: 7 May 2009

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Zentralblatt MATH identifier

Primary: 62P05: Applications to actuarial sciences and financial mathematics 60J75: Jump processes
Secondary: 93E20: Optimal stochastic control

Optimal portfolio jumps Merton problem factor models closed-form solution


Aït-Sahalia, Yacine; Cacho-Diaz, Julio; Hurd, T. R. Portfolio choice with jumps: A closed-form solution. Ann. Appl. Probab. 19 (2009), no. 2, 556--584. doi:10.1214/08-AAP552.

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