The Annals of Applied Probability

Portfolios and risk premia for the long run

Paolo Guasoni and Scott Robertson

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This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete. Investment opportunities are driven by, and partially correlated with, state variables which follow an autonomous diffusion. The framework nests models of stochastic interest rates, return predictability, stochastic volatility and correlation risk.

In models with several assets and a single state variable, long-run portfolios and risk premia admit explicit formulas up the solution of an ordinary differential equation which characterizes the principal eigenvalue of an elliptic operator. Multiple state variables lead to a quasilinear partial differential equation which is solvable for many models of interest.

The paper derives the long-run optimal portfolio and the long-run optimal pricing measures depending on relative risk aversion, as well as their finite-horizon performance.

Article information

Ann. Appl. Probab. Volume 22, Number 1 (2012), 239-284.

First available in Project Euclid: 7 February 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91G10: Portfolio theory 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 91G20: Derivative securities

Long-run portfolio choice derivatives pricing incomplete markets


Guasoni, Paolo; Robertson, Scott. Portfolios and risk premia for the long run. Ann. Appl. Probab. 22 (2012), no. 1, 239--284. doi:10.1214/11-AAP767.

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