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Duality In Optimal Investment And Consumption Problems With Market Frictions

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  • I. Klein
  • L. C. G. Rogers

Abstract

In the style of Rogers (2001), we give a unified method for finding the dual problem in a given model by stating the problem as an unconstrained Lagrangian problem. In a theoretical part we prove our main theorem, Theorem 3.1, which shows that under a number of conditions the value of the dual and primal problems is equal. The theoretical setting is sufficiently general to be applied to a large number of examples including models with transaction costs, such as Cvitanic and Karatzas (1996) (which could not be covered by the setting in Rogers [2001]). To apply the general result one has to verify the assumptions of Theorem 3.1 for each concrete example. We show how the method applies for two examples, first Cuoco and Liu (1992) and second Cvitanic and Karatzas (1996).

Suggested Citation

  • I. Klein & L. C. G. Rogers, 2007. "Duality In Optimal Investment And Consumption Problems With Market Frictions," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 225-247, April.
    • Handle: RePEc:bla:mathfi:v:17:y:2007:i:2:p:225-247
    DOI: 10.1111/j.1467-9965.2006.00301.x
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    Cited by:

    1. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    2. Luciano Campi & Mark Owen, 2011. "Multivariate utility maximization with proportional transaction costs," Finance and Stochastics, Springer, vol. 15(3), pages 461-499, September.
    3. Teemu Pennanen & Ari-Pekka Perkkiö, 2018. "Convex duality in optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 22(4), pages 733-771, October.
    4. Teemu Pennanen & Ari-Pekka Perkkio, 2016. "Convex duality in optimal investment and contingent claim valuation in illiquid markets," Papers 1603.02867, arXiv.org.
    5. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.
    6. Wing Fung Chong & Gechun Liang, 2018. "Optimal investment and consumption with forward preferences and uncertain parameters," Papers 1807.01186, arXiv.org, revised Nov 2023.
    7. Nguyen-Thanh Long, 2004. "Investment optimization under constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 175-201, October.
    8. Mauricio Junca & Rafael Serrano, 2014. "Utility maximization in pure-jump models driven by marked point processes and nonlinear wealth dynamics," Papers 1411.1103, arXiv.org, revised Sep 2015.
    9. Hugo E. Ramirez & Rafael Serrano, 2023. "Optimal investment with insurable background risk and nonlinear portfolio allocation frictions," Papers 2303.04236, arXiv.org.
    10. Kristina Rognlien Dahl, 2019. "A convex duality approach for pricing contingent claims under partial information and short selling constraints," Papers 1902.10492, arXiv.org.
    11. Teemu Pennanen, 2011. "Convex Duality in Stochastic Optimization and Mathematical Finance," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 340-362, May.
    12. Long Nguyen-Thanh, 2002. "Consumption and Investment Optimization under Constraints," Finance 0211004, University Library of Munich, Germany, revised 25 Mar 2003.
    13. Ramírez, H & Serrano, R, 2023. "Optimal investment with insurable background risk and nonlinear portfolio allocation frictions," Documentos de Trabajo 20658, Universidad del Rosario.
    14. repec:dau:papers:123456789/2318 is not listed on IDEAS

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