Most decision theories  including expected utility theory, rank dependent utility theory and the cumulative prospect theory  assume that investors are only interested in the distribution of returns and not about 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  is often at odds with the needs of many investors. We introduce a framework for portfolio selection that permits to deal with state-dependent preferences . We are able to characterize optimal payoffs in explicit form. Some applications in security design are discussed in detail. We extend the classical expected utility optimization problem of Merton to the state-dependent situation and also give some stochastic extensions of the target probability optimization problem.
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.
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