Portfolio choice with jumps: A closed-form solution

TL;DR

This paper derives a closed-form solution for optimal portfolio choice considering both continuous Brownian risks and discrete jump risks, highlighting the importance of managing jump exposure.

Contribution

It introduces orthogonal decomposition techniques to solve the consumption-portfolio problem with jumps, providing a novel analytical approach.

Findings

Optimal policy emphasizes controlling jump risk exposure.

Orthogonal decompositions simplify the portfolio optimization problem.

Closed-form solutions enable practical implementation.

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.