Twisted Probabilities, Uncertainty, and Prices

55 Pages Posted: 15 Jan 2019

See all articles by Lars Peter Hansen

Lars Peter Hansen

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

Balint Szoke

NYU

Lloyd S. Han

University of Chicago

Thomas J. Sargent

New York University (NYU) - Department of Economics, Leonard N. Stern School of Business; National Bureau of Economic Research (NBER)

Date Written: January 14, 2019

Abstract

A decision maker constructs a convex set of nonnegative martingales to use as likelihood ratios that represent alternatives that are statistically close to a decision maker's baseline model. The set is twisted to include some specific models of interest. Max-min expected utility over that set gives rise to equilibrium prices of model uncertainty expressed as worst-case distortions to drifts in a representative investor's baseline model. Three quantitative illustrations start with baseline models having exogenous long-run risks in technology shocks. These put endogenous long-run risks into consumption dynamics that differ in details that depend on how shocks affect returns to capital stocks. We describe sets of alternatives to a baseline model that generate countercyclical prices of uncertainty.

Keywords: Risk, uncertainty, relative entropy, robustness, asset prices, exponential quadratic stochastic discount factor

JEL Classification: C52, C58, D81, D84, G12

Suggested Citation

Hansen, Lars Peter and Szoke, Balint and Han, Lloyd S. and Sargent, Thomas J., Twisted Probabilities, Uncertainty, and Prices (January 14, 2019). University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2019-02. Available at SSRN: https://ssrn.com/abstract=3314356 or http://dx.doi.org/10.2139/ssrn.3314356

Lars Peter Hansen (Contact Author)

University of Chicago - Department of Economics ( email )

1101 E 58th ST
Chicago, IL 60637
United States
773-702-8170 (Phone)
773-702-8490 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Balint Szoke

NYU ( email )

19 West 4th Street
New York, NY 10003
United States

Lloyd S. Han

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Thomas J. Sargent

New York University (NYU) - Department of Economics, Leonard N. Stern School of Business ( email )

269 Mercer Street
New York, NY 10003
United States
212-998-3548 (Phone)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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