| | |
Summary: The Annals of Applied Probability
2009, Vol. 19, No. 2, 556584
DOI: 10.1214/08-AAP552
© Institute of Mathematical Statistics, 2009
PORTFOLIO CHOICE WITH JUMPS:
A CLOSED-FORM SOLUTION
BY YACINE AÏT-SAHALIA,1 JULIO CACHO-DIAZ AND T. R. HURD2
Princeton University, Princeton University and McMaster University
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.
1. Introduction. Economists have long been aware of the potential benefits
of international diversification, while at the same time noting that the portfolios
held by actual investors typically suffer from a home bias effect, meaning that
those portfolios tend to be less diversified internationally than would be opti-
mal according to portfolio choice theory [see, e.g., Solnik (1974) and Grauer and
|
