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Cost-efficiency in Incomplete Markets

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  • Carole Bernard
  • Stephan Sturm

Abstract

This paper studies the topic of cost-efficiency in incomplete markets. A payoff is called cost-efficient if it achieves a given probability distribution at some given investment horizon with a minimum initial budget. Extensive literature exists for the case of a complete financial market. We show how the problem can be extended to incomplete markets and how the main results from the theory of complete markets still hold in adapted form. In particular, we find that in incomplete markets, the optimal portfolio choice for non-decreasing preferences that are diversification-loving (a notion introduced in this paper) must be "perfectly" cost-efficient. This notion of perfect cost-efficiency is shown to be equivalent to the fact that the payoff can be rationalized, i.e., it is the solution to an expected utility problem.

Suggested Citation

  • Carole Bernard & Stephan Sturm, 2022. "Cost-efficiency in Incomplete Markets," Papers 2206.12511, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2206.12511
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    File URL: http://arxiv.org/pdf/2206.12511
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    References listed on IDEAS

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    1. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
    2. B. Bouchard & N. Touzi & A. Zeghal, 2004. "Dual formulation of the utility maximization problem: the case of nonsmooth utility," Papers math/0405290, arXiv.org.
    3. Philip H. Dybvig, 1988. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 67-88.
    4. repec:dau:papers:123456789/1531 is not listed on IDEAS
    5. Bernard Carole & Vanduffel Steven, 2015. "Quantile of a Mixture with Application to Model Risk Assessment," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-10, October.
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    Cited by:

    1. Mauricio Elizalde & Stephan Sturm, 2024. "Intertemporal Cost-efficient Consumption," Papers 2405.16336, arXiv.org.

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