On the Construction of Optimal Payoffs

29 Pages Posted: 9 Mar 2017  

Ludger Rüschendorf

University of Freiburg

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: March 9, 2017

Abstract

We show that any problem of optimal payoff (portfolio) choice under an increasing law-invariant objective function can be reduced to an optimization problem for real functions under monotonicity restrictions. We solve some of these optimization problems and apply the results to solve several portfolio selection problems of interest. In particular, we completely describe the optimal payoff for an investor with preferences as in Yaari’s Dual Theory of Choice. We extend the reduction result to the case in which the payoff is required to have a fixed copula with some benchmark (state-dependent constraint). Specifically, we show that if one can determine the optimal payoff under a law-invariant objective, then one can also determine the optimal payoff when adding the state-dependent constraint. We also describe a setting with market specified prices that is rich enough to ensure attainability of the optimal payoff by means of a static portfolio of puts and calls.

Keywords: Optimal portfolio selection, State-dependent preferences, Conditional distribution, Yaari’s dual theory of choice, Incompleteness

Suggested Citation

Rüschendorf, Ludger and Vanduffel, Steven, On the Construction of Optimal Payoffs (March 9, 2017). Available at SSRN: https://ssrn.com/abstract=2930046

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Steven Vanduffel (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

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