Title: Optimal payoffs under state-dependent preferences
Journal Title: Quantitative Finance
Volume: pages 1-17
Issue: pages 1-17
Publication Date: pages 1-17
Start Page: pages1-17
End Page: pages1-17
a Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L3G1, Canada.
b CREM and IGR-IAE de Rennes, Univ. Rennes 1, 11 rue Jean Macé, 35000 Rennes, France.
c Department Mathematical Stochastics, University of Freiburg, Eckerstra?e 1, 79104 Freiburg, Germany.
d Department of Economics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Bruxelles, Belgium.
Abstract: Most decision theories, including expected utility theory, rank-dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors. We introduce a framework for portfolio selection within which state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize Optimal payoffs in explicit form. Furthermore, we extend the classical expected utility optimization problem of Merton to the state-dependent situation. Some applications in security design are discussed in detail and we also solve some stochastic extensions of the target probability optimization problem.
Accepted: 16 Oct 2014
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