Dynamically Consistent α-Maxmin Expected Utility

25 Pages Posted: 11 Feb 2015 Last revised: 29 Feb 2016

See all articles by Patrick Beissner

Patrick Beissner

Bielefeld University - Center for Mathematical Economics

Qian Lin

Bielefeld University - Center for Mathematical Economics

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Date Written: February 13, 2016

Abstract

The α-maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of α. In this paper, we derive a recursive, dynamically consistent version of the α-maxmin model. In the continuous-time limit, the resulting dynamic utility function can be represented as a convex mixture between worst and best case, but now at the local, infinitesimal level.

We study the properties of the utility function and provide an Arrow-Pratt approximation of the static and dynamic certainty equivalent. We derive a consumption-based capital asset pricing formula and study the implications for derivative valuation under indifference pricing.

Keywords: Dynamic consistency, α maxmin expected utility, Knightian uncertaint, ambiguity attitude

JEL Classification: C60, D81, D90

Suggested Citation

Beissner, Patrick and Lin, Qian and Riedel, Frank, Dynamically Consistent α-Maxmin Expected Utility (February 13, 2016). Center for Mathematical Economics Working Paper No. 535. Available at SSRN: https://ssrn.com/abstract=2562354 or http://dx.doi.org/10.2139/ssrn.2562354

Patrick Beissner (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Qian Lin

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Frank Riedel

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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