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Portfolio Choice in Markets with Contagion

33 Pages Posted: 5 Oct 2012 Last revised: 27 Mar 2015

Yacine Ait-Sahalia

Princeton University - Department of Economics; National Bureau of Economic Research (NBER)

Thomas R. Hurd

McMaster University - Department of Mathematics and Statistics

Date Written: March 26, 2015

Abstract

We consider the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes. This captures a type of contagion where each downward jump in an asset's price results in increased likelihood of further jumps, both in that asset and in the other assets. We solve in closed-form the dynamic consumption-investment problem of a log-utility investor in such a contagion model, prove a theorem verifying its optimality and discuss features of the solution, including flight-to-quality. The exponential and power utility investors are also considered: in these cases, the optimal strategy can be characterized as a distortion of the strategy of a corresponding non-contagion investor.

Keywords: Merton problem, jumps, Hawkes process, mutual excitation, contagion, flight-to-quality

JEL Classification: G11, G01

Suggested Citation

Ait-Sahalia, Yacine and Hurd, Thomas R., Portfolio Choice in Markets with Contagion (March 26, 2015). Available at SSRN: https://ssrn.com/abstract=2157038 or http://dx.doi.org/10.2139/ssrn.2157038

Yacine Ait-Sahalia

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Princeton University - Department of Economics ( email )

Fisher Hall
Princeton, NJ 08544
United States
609-258-4015 (Phone)
609-258-5398 (Fax)

Thomas R. Hurd (Contact Author)

McMaster University - Department of Mathematics and Statistics ( email )

Canada

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