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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Abstract

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

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

Dates
First available in Project Euclid: 7 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1241702241

Digital Object Identifier
doi:10.1214/08-AAP552

Mathematical Reviews number (MathSciNet)
MR2521879

Zentralblatt MATH identifier
1170.91364

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

Keywords
Optimal portfolio jumps Merton problem factor models closed-form solution

Citation

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. https://projecteuclid.org/euclid.aoap/1241702241


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Annals of Applied Probability

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