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Optimal claims with fixed payoff structure

Part of: Mathematical economics Mathematical finance

Published online by Cambridge University Press:  30 March 2016

Carole Bernard ,
Ludger Rüschendorf  and
Steven Vanduffel
Carole Bernard
Affiliation:
University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L3G1, Canada. Email address: c3bernar@uwaterloo.ca.
Ludger Rüschendorf
Affiliation:
University of Freiburg, Eckerstraße 1, 79104 Freiburg, Germany. Email address: ruschen@stochastik.uni-freiburg.de.
Steven Vanduffel
Affiliation:
Vrije Universiteit Brussel, Pleinlaan 2, 1050 Bruxelles, Belgium. Email address: steven.vanduffel@vub.ac.be.
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Abstract

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Dybvig (1988) introduced the interesting problem of how to construct in the cheapest possible way a terminal wealth with desired distribution. This idea has induced a series of papers concerning generality, consequences, and applications. As the optimized claims typically follow the trend in the market, they are not useful for investors who wish to use them to protect an existing portfolio. For this reason, Bernard, Moraux, Rüschendorf and Vanduffel (2014b) imposed additional state-dependent constraints as a way of controlling the payoff structure. The present paper extends this work in various ways. In order to obtain optimal claims in general models we allow in this paper for extended contracts. We deal with general multivariate price processes and dispense with several of the regularity assumptions in the previous work (in particular, we omit any continuity assumption). State dependence is modeled by requiring terminal wealth to have a fixed copula with a benchmark wealth. In this setting, we are able to characterize optimal claims. We apply the theoretical results to deal with several hedging and expected utility maximization problems of interest.

Keywords

Cost-efficient payoffoptimal portfoliostate-dependent utility

MSC classification

Primary: 91G10: Portfolio theory 91B16: Utility theory
Type
Part 5. Finance and econometrics
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 175 - 188
Copyright
Copyright © Applied Probability Trust 2014 

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