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On the construction of optimal payoffs

L. Rüschendorf () and Steven Vanduffel ()
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L. Rüschendorf: University of Freiburg
Steven Vanduffel: Vrije Universiteit Brussel

Decisions in Economics and Finance, 2020, vol. 43, issue 1, No 9, 129-153

Abstract: Abstract In the framework of continuous-time market models with specified pricing density, optimal payoffs under increasing law-invariant preferences are known to be anti-monotonic with the pricing density. Consequently, optimal portfolio selection problems can be reformulated as optimization problems on real functions under monotonicity conditions. We solve two basic types of these optimization problems, which makes it possible to obtain in a fairly unified way the optimal payoff for several portfolio selection problems of interest. In particular, we completely solve the optimal portfolio selection problem for an investor with preferences as in cumulative prospect theory or as in Yaari’s dual theory. Extending previous work, we also characterize optimal payoffs when 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 concave law-invariant objective, then one can also determine the optimal payoff when adding the state-dependent constraint. In the final part of the paper, we consider an extension to (incomplete) market models in which the pricing density is not completely specified. When a sufficient number of payoffs have a known market price, we show that optimal payoffs are anti-monotonic to some pricing density that we explicitly derive from these market prices. As examples, we deal with some exponential Lévy market models and some market models involving Itô processes.

Keywords: State-dependent preferences; Yaari’s dual theory of choice; Incomplete market models; Optimization under monotonicity constraints; Hoeffding–Fréchet bounds; 91B28; 91B30; 91B02 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10203-019-00272-9

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