Optimal claims with fixed payoff structure

Dybvig ? 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 et al. ? impose additional state-dependent constraints as a way of controlling the payoff structure. The present paper extends this work in various ways. In order to get optimal claims in general models we allow in this paper for extended contracts. We deal with general multivariate price processes and dismiss with several of the regularity assumptions in the previous work (in particular, we omit any continuity assumption). State-dependence is modeled by requiring that terminal wealth has 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. Key-words: cost-efficient payoffs, optimal portfolio, state-dependent utilities AMS classification: 91G10, 91B16