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Local risk-minimization under transaction costs


  • Lamberton, Damien
  • Pham, Huyên
  • Schweizer, Martin


We propose a new approach to the pricing and hedging of contingent claims under transaction costs in a general incomplete market in discrete time. Under the assumptions of a bounded mean-variance tradeoff, substantial risk and a nondegeneracy condition on the conditional variances of asset returns, we prove the existence of a locally risk-minimizing strategy inclusive of transaction costs for every square-integrable contingent claim. Then we show that local riskminimization is robust under the inclusion of transaction costs: The preceding strategy which is locally risk-minimizing inclusive of transaction costs in a model with bid-ask spreads on the underlying asset is also locally risk-minimizing without transaction costs in a fictitious model which is frictionless and where the fictitious asset price lies between the bid and ask price processes of the original model. In particular, our results apply to any nondegenerate model with a finite state space if the transaction cost parameter is sufficiently small.

Suggested Citation

  • Lamberton, Damien & Pham, Huyên & Schweizer, Martin, 1998. "Local risk-minimization under transaction costs," SFB 373 Discussion Papers 1998,18, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:199818

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    References listed on IDEAS

    1. Dial, Jay & Murphy, Kevin J., 1995. "Incentives, downsizing, and value creation at General Dynamics," Journal of Financial Economics, Elsevier, vol. 37(3), pages 261-314, March.
    2. Paul L. Joskow & Nancy L. Rose, 1994. "CEO Pay and Firm Performance: Dynamics, Asymmetries, and Alternative Performance Measures," NBER Working Papers 4976, National Bureau of Economic Research, Inc.
    3. Peter F. Kostiuk, 1990. "Firm Size and Executive Compensation," Journal of Human Resources, University of Wisconsin Press, vol. 25(1), pages 90-105.
    4. Jensen, Michael C & Murphy, Kevin J, 1990. "Performance Pay and Top-Management Incentives," Journal of Political Economy, University of Chicago Press, vol. 98(2), pages 225-264, April.
    5. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
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    Cited by:

    1. Jin Hyuk Choi & Mihai Sirbu & Gordan Zitkovic, 2012. "Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs," Papers 1204.0305,, revised Jun 2012.
    2. Jan Kallsen & Johannes Muhle-Karbe, 2011. "Existence of shadow prices in finite probability spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 251-262, April.
    3. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    4. Eric Beutner, 2007. "Mean–variance hedging under transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 539-557, June.
    5. repec:spr:compst:v:73:y:2011:i:2:p:251-262 is not listed on IDEAS
    6. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    7. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the Existence of Shadow Prices," Papers 1111.6633,, revised Jan 2013.
    8. Pansera, Jérôme, 2012. "Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 1-11.
    9. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2013. "On the existence of shadow prices," Finance and Stochastics, Springer, vol. 17(4), pages 801-818, October.
    10. repec:wsi:ijfexx:v:04:y:2017:i:02n03:n:s242478631750030x is not listed on IDEAS
    11. repec:spr:compst:v:65:y:2007:i:3:p:539-557 is not listed on IDEAS
    12. Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2017. "Quadratic hedging with multiple assets under illiquidity with applications in energy markets," Papers 1705.06918,
    13. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    14. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the existence of shadow prices," Working Papers hal-00645980, HAL.

    More about this item


    option pricing; hedging; transaction costs; locally risk-minimizing strategies; mean-variance tradeoff;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General


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