Distributional Analysis of Portfolio Choice

Efficient portfolios in financial markets with proportional transaction costs

“…This theorem considerably generalizes previous results in Dybvig [9,10] and in Jouini and Kallal [17]. Moreover, following Jouini and Kallal [17], we compute for every contingent claim a measure of inefficiency that does not refer to any specific utility functions, using the anticomonotonicity property.…”

“…It is natural in this framework to introduce the following set 9) to describe the set of all (positive) contingent claims which are better than X 0 for all those agents whose preferences belong to U. We can now state the main result of this section, giving in particular in (ii) a dual representation of the utility price.…”

“…The notion of portfolio's efficiency goes back to a couple of articles by Dybvig [9,10], where he studies those strategies that are chosen by at least one rational agent in a simple frictionless complete market with finitely many and equiprobable states of the world. In this context, the no-arbitrage condition is equivalent to the existence of a unique linear pricing rule and -this is Dybvig's result -a consumption bundle is efficient if and only if it provides at least as much consumption in cheaper states of the world (according to the unique risk-neutral pricing rule).…”

Utility Maximization Under Solvency Constraints and Unhedgeable Risks

“…The following lemma states this result, in the sense that our optimal terminal wealth (the "lottery") is a non-increasing function of the state price deflator. Although, this is just the result already obtained by Dybvig (1988), we provide the proof in the context of this paper.…”

“…Dybvig (1988) has shown that "any cheapest way to achieve a lottery assigns the outcomes of the lottery to the states in reverse order of the state-price density...". The following lemma states this result, in the sense that our optimal terminal wealth (the "lottery") is a non-increasing function of the state price deflator.…”