Stochastic Compounding and Uncertain Valuation

30 Pages Posted: 24 Apr 2013 Last revised: 11 Feb 2016

Lars Peter Hansen

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

Jose A. Scheinkman

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

Multiple version iconThere are 2 versions of this paper

Date Written: January 31, 2016

Abstract

Exploring long-term implications of valuation leads us to recover and use a distorted probability measure that reflects the long-term implications for risk pricing. This measure is typically distinct from the physical and the risk neutral measures that are well known in mathematical finance. We apply a generalized version of Perron-Frobenius theory to construct this probability measure and present several applications. We employ Perron-Frobenius methods to i) explore the observational implications of risk adjustments and investor beliefs as reflected in asset market data; ii) catalog alternative forms of misspecification of parametric valuation models; and iii) characterize how long-term components of growth-rate risk impact investor preferences implied by Kreps-Porteus style utility recursions.

Keywords: Perron-Frobenius, martingale component of stochastic discount factor, long-term risk pricing

JEL Classification: G12

Suggested Citation

Hansen, Lars Peter and Scheinkman, Jose A., Stochastic Compounding and Uncertain Valuation (January 31, 2016). Available at SSRN: https://ssrn.com/abstract=2256246 or http://dx.doi.org/10.2139/ssrn.2256246

Lars Peter Hansen

National Bureau of Economic Research (NBER)

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University of Chicago - Department of Economics ( email )

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Jose A. Scheinkman (Contact Author)

Columbia University ( email )

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Princeton University - Department of Economics ( email )

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HOME PAGE: http://www.princeton.edu/~joses

National Bureau of Economic Research (NBER)

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United States

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