A Neyman-Pearson Problem with Ambiguity and Nonlinear Pricing

Mathematics and Financial Economics, Forthcoming

21 Pages Posted: 5 Dec 2017

Date Written: November 23, 2017

Abstract

We consider a problem of the Neyman-Pearson type arising in the theory of portfolio choice in the presence of probability weighting, such as in markets with Choquet pricing (as in Araujo et al (2011), Cerreia-Vioglio et al (2015), Chateauneuf and Cornet (2015), or Chateauneuf et al (1996)) and ambiguous beliefs about the payoffs of contingent claims. Specifically, we consider a problem of optimal choice of a contingent claim so as to minimize a non-linear pricing functional (or a distortion risk measure), subject to a minimum expected performance measure (or a minimum expected return or utility), where expectations with respect to distorted probabilities are taken in the sense of Choquet. Such contingent claims are called cost-efficient. We give an analytical characterization of cost-efficient contingent claims under very mild assumptions on the probability weighting functions, thereby extending some of the results of Ghossoub (2016), and we provide examples of some special cases of interest as well as an illustrative numerical example. In particular, we show how a cost-efficient contingent claim exhibits a desirable monotonicity property: It is anti-comonotonic with the random mark-to-market value (or return, etc.) of the underlying financial position, and it is hence a hedge against such variability.

Suggested Citation

Ghossoub, Mario, A Neyman-Pearson Problem with Ambiguity and Nonlinear Pricing (November 23, 2017). Mathematics and Financial Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=3014957

Mario Ghossoub (Contact Author)

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1
Canada

HOME PAGE: http://uwaterloo.ca/scholar/mghossou

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