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February 2012 Portfolios and risk premia for the long run
Paolo Guasoni, Scott Robertson
Ann. Appl. Probab. 22(1): 239-284 (February 2012). DOI: 10.1214/11-AAP767


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.


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Paolo Guasoni. Scott Robertson. "Portfolios and risk premia for the long run." Ann. Appl. Probab. 22 (1) 239 - 284, February 2012.


Published: February 2012
First available in Project Euclid: 7 February 2012

zbMATH: 1247.91172
MathSciNet: MR2932547
Digital Object Identifier: 10.1214/11-AAP767

Primary: 62P05, 91G10
Secondary: 91G20

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.22 • No. 1 • February 2012
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