Representation Theory for Risk on Markowitz-Tversky-Kahneman Topology

27 Pages Posted: 11 Jun 2012 Last revised: 12 Jun 2012

See all articles by G. Charles-Cadogan

G. Charles-Cadogan

University of Leicester; Ryerson University - Institute for Innovation and Technology Management

Date Written: June 10, 2012

Abstract

We introduce a representation theory for risk operations on locally compact groups in a partition of unity on a topological manifold for Markowitz-Tversky-Kahneman (MTK) reference points. We identify (1) risk torsion induced by the flip rate for risk averse and risk seeking behavior, and (2) a structure constant or coupling of that torsion in the paracompact manifold. The risk torsion operator extends by continuity to prudence and maxmin expected utility (MEU) operators, as well as other behavioral operators introduced by the Italian school. In our erstwhile chaotic dynamical system, induced by behavioral rotations of probability domains, the loss aversion index is an unobserved gauge transformation; and reference points are hyperbolic on the utility hypersurface characterized by the special unitary group SU(n). We identify conditions for existence of harmonic utility functions on paracompact MTK manifolds induced by transformation groups. And we use those mathematical objects to estimate: (1) loss aversion index from infinitesimal tangent vectors; and (2) value function from a classic Dirichlet problem for first exit time of Brownian motion from regular points on the boundary of MTK base topology.

Keywords: representation theory, topological groups, utility hypersurface, risk torsion, chaos, loss aversion

JEL Classification: C62, C65, D81

Suggested Citation

Charles-Cadogan, G., Representation Theory for Risk on Markowitz-Tversky-Kahneman Topology (June 10, 2012). Available at SSRN: https://ssrn.com/abstract=2081376 or http://dx.doi.org/10.2139/ssrn.2081376

G. Charles-Cadogan (Contact Author)

University of Leicester ( email )

University Road
Leicester, LE1 7RH
United Kingdom

Ryerson University - Institute for Innovation and Technology Management ( email )

575 Bay
Toronto, Ontario M5G 2C5
Canada

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