We examine a class of utility maximization problems with a non-necessarily law-invariant utility, and with a non-necessarily law-invariant risk measure constraint. Under a consistency requirement on the risk measure that we call Vigilance, we show the existence of optimal contingent claims, and...

At any given point in time, the collection of assets existing in the economy is observable. Each asset is a function of a set of contingencies. The union taken over all assets of these contingencies is what we call the set of publicly known states. An innovation is a set of states that are not...

I examine a class of utility maximization problems with a not necessarily law-invariant utility, and with a not necessarily law-invariant risk measure constraint. The objective function is an integral of some function U with respect to some probability measure P, and the constraint set contains...

We derive the optimal portfolio choice for an investor who behaves according to Cumulative Prospect Theory. The study is done in a one-period economy with one risk-free asset and one risky asset, and the reference point corresponds to the terminal wealth arising when the entire initial wealth is...

At any given point in time, the collection of assets existing in the economy is observable. Each asset is a function of a set of contingencies. The union taken over all assets of these contingencies is what we call the set of publicly known states. An innovation is a set of states that are not...

In complete frictionless securities markets under uncertainty, it is well-known that in the absence of arbitrage opportunities, there exists a unique linear positive pricing rule, which induces a state-price density (e.g., Harrison and Kreps (1979)). Dybvig (1988) showed that the cheapest way to...

Arrow's classical result on the optimality of the deductible indemnity schedule holds in a situation where the insurer is a risk-neutral Expected-Utility (EU) maximizer, the insured is a risk-averse EU-maximizer, and the two parties share the same probabilistic beliefs about the realizations of...

In the classical Expected-Utility framework, a problem of optimal insurance design with a premium constraint is equivalent to a problem of optimal insurance design with a minimum expected retention constraint. When the insurer has ambiguous beliefs represented by a non-additive probability...

We consider a problem of the Neyman-Pearson type arising in the theory of portfolio choice in the presence of probability weighting, such as in markets with Choquet pricing (as in Araujo et al (2011), Cerreia-Vioglio et al (2015), Chateauneuf and Cornet (2015), or Chateauneuf et al (1996)) and...

I examine a class of utility maximization problems with a not necessarily law-invariant utility, and with a not necessarily law-invariant risk measure constraint. The objective function is a Lebesgue integral of some function U with respect to some probability measure P, and the constraint set...