Multivariate utility maximization with proportional transaction costs

Campi, Luciano; Owen, Mark P.

doi:10.1007/s00780-010-0125-9

Cited by 40 publications

(71 citation statements)

References 28 publications

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“…The choice of multivariate utility functions reflects the idea that the agents will not necessarily liquidate their positions to a single numeraire at the final date (which is realistic, in particular, on a currency market). This is coherent with the recent papers [1,3] dealing with optimal investment problem under frictions. Moreover, it allows us to rely upon the duality methods developed therein.…”

Section: Introductionsupporting

confidence: 89%

“…Thus we do not need to impose regularity conditions on the utility functions. That's why we will use instead recent results established in Campi and Owen [3], which seem to be more suitable for our purposes.…”

Section: Characterization Of Efficient Trading Strategiesmentioning

confidence: 99%

“…We will make use of the duality result that has been established in Campi and Owen [3]. To do that, we recall once more that D denotes the dual cone of…”

Section: Characterization Of Efficient Strategiesmentioning

confidence: 99%

“…For reader's convenience, we collect in the next proposition the results in [3] that we are going to use in the proofs. The next proposition states in particular that there is no duality gap between primal and a (suitably defined) dual problem provided the initial portfolio x does not lie on the boundary of dom(u), and that the dual problem has a solution whenever x lies in the interior of dom(u).…”

Section: Characterization Of Efficient Strategiesmentioning

confidence: 99%

“…In this paper we characterize efficient portfolios in a general multivariate financial market with transaction costs as in [28,4,3], where agents can trade in finitely many risky assets (e.g. foreign currency) facing transaction costs at each trading.…”

Section: Introductionmentioning

confidence: 99%

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Efficient portfolios in financial markets with proportional transaction costs

2013

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In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general financial market model with proportional transaction costs. In our setting, transaction costs may be random, time-dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. Thanks to the dual formulation of expected multivariate utility maximization problem established in Campi and Owen [3], we provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig [10] and Jouini and Kallal [16]. We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading in the market, and give a dual representation of it.

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Section: Introductionsupporting

confidence: 89%

Section: Characterization Of Efficient Trading Strategiesmentioning

confidence: 99%

“…We will make use of the duality result that has been established in Campi and Owen [3]. To do that, we recall once more that D denotes the dual cone of…”

Section: Characterization Of Efficient Strategiesmentioning

confidence: 99%

Section: Characterization Of Efficient Strategiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient portfolios in financial markets with proportional transaction costs

2013

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Existence of shadow prices in finite probability spaces

Kallsen

Muhle‐Karbe

2011

Math Meth Oper Res

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A shadow price is a process S lying within the bid/ask prices S, S of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with price process S leads to the same maximal utility as in the original market with transaction costs. For finite probability spaces, this note provides an elementary proof for the existence of such a shadow price.

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A set optimization approach to zero-sum matrix games with multi-dimensional payoffs

Hamel

Löhne

2018

Math Meth Oper Res

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A new solution concept for two-player zero-sum matrix games with multidimensional payoff is introduced. It is based on extensions of the vector order in R K to order relations in the power set of R K , so-called set relations, and strictly motivated by the interpretation of the payoff as multi-dimensional loss for one and gain for the other player. The new concept provides coherent worst case estimates, i.e. minimax and maximin strategies, for games with multi-dimensional payoffs. It is shown that-in contrast to games with one-dimensional payoffs-minimax/maximin strategies are independent from Shapley's notion of equilibrium strategies for such games. Therefore, the two concepts are combined into new equilibrium notions for which existence theorems are given. By means of examples, relationships of the new concepts to existing ones such as Shapley and vector equilibria, vector minimax/maximin solutions and Pareto optimal security strategies are clarified. A algorithm for computing optimal strategies is presented.

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Multivariate utility maximization with proportional transaction costs

Abstract: Transaction costs, Foreign exchange market, Multivariate utility function, Asymptotic satiability, Optimal portfolio, Duality theory, Lagrange duality, 91B28, 49N15, 49J40, 49J55, G11,

Cited by 40 publications

References 28 publications

Efficient portfolios in financial markets with proportional transaction costs

Efficient portfolios in financial markets with proportional transaction costs

Existence of shadow prices in finite probability spaces

A set optimization approach to zero-sum matrix games with multi-dimensional payoffs

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