IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2311.08871.html
   My bibliography  Save this paper

A short note on super-hedging an arbitrary number of European options with integer-valued strategies

Author

Listed:
  • Dorsaf Cherif
  • Meriam El Mansour
  • Emmanuel Lepinette

Abstract

The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance. This is clearly contrary to what it is possible to do in the real world. Surprisingly, it seems that there is no many contributions in that direction in the literature, except for a finite number of states. In this paper, for arbitrary {\Omega}, we show that, in discrete-time, it is possible to evaluate the minimal super-hedging price when we restrict ourselves to integer-valued strategies. To do so, we only consider terminal claims that are continuous piecewise affine functions of the underlying asset. We formulate a dynamic programming principle that can be directly implemented on an historical data and which also provides the optimal integer-valued strategy. The problem with general payoffs remains open but should be solved with the same approach.

Suggested Citation

  • Dorsaf Cherif & Meriam El Mansour & Emmanuel Lepinette, 2023. "A short note on super-hedging an arbitrary number of European options with integer-valued strategies," Papers 2311.08871, arXiv.org.
    • Handle: RePEc:arx:papers:2311.08871
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2311.08871
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    2. Meriam El Mansour & Emmanuel Lépinette, 2020. "Conditional Interior and Conditional Closure of Random Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 356-369, November.
    3. Stefan Gerhold & Paul Krühner, 2018. "Dynamic trading under integer constraints," Finance and Stochastics, Springer, vol. 22(4), pages 919-957, October.
    4. Philipp Baumann & Norbert Trautmann, 2013. "Portfolio-optimization models for small investors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 345-356, June.
    5. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stefan Gerhold & Paul Kruhner, 2017. "Dynamic trading under integer constraints," Papers 1708.07661, arXiv.org.
    2. Stefan Gerhold & Paul Krühner, 2018. "Dynamic trading under integer constraints," Finance and Stochastics, Springer, vol. 22(4), pages 919-957, October.
    3. Miguel A. Lejeune & François Margot, 2016. "Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities," Operations Research, INFORMS, vol. 64(4), pages 939-957, August.
    4. Xueting Cui & Xiaoling Sun & Shushang Zhu & Rujun Jiang & Duan Li, 2018. "Portfolio Optimization with Nonparametric Value at Risk: A Block Coordinate Descent Method," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 454-471, August.
    5. Panos Xidonas & Christis Hassapis & George Mavrotas & Christos Staikouras & Constantin Zopounidis, 2018. "Multiobjective portfolio optimization: bridging mathematical theory with asset management practice," Annals of Operations Research, Springer, vol. 267(1), pages 585-606, August.
    6. Dimitris Bertsimas & Ryan Cory-Wright, 2022. "A Scalable Algorithm for Sparse Portfolio Selection," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1489-1511, May.
    7. Amir Ahmadi-Javid & Pooya Hoseinpour, 2022. "Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2621-2633, September.
    8. Ran Ji & Miguel A. Lejeune, 2021. "Data-Driven Optimization of Reward-Risk Ratio Measures," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1120-1137, July.
    9. Murray, Chase C. & Talukdar, Debabrata & Gosavi, Abhijit, 2010. "Joint Optimization of Product Price, Display Orientation and Shelf-Space Allocation in Retail Category Management," Journal of Retailing, Elsevier, vol. 86(2), pages 125-136.
    10. Zhi-Hai Zhang & Kang Li, 2015. "A novel probabilistic formulation for locating and sizing emergency medical service stations," Annals of Operations Research, Springer, vol. 229(1), pages 813-835, June.
    11. Ran Ji & Miguel A. Lejeune, 2018. "Risk-budgeting multi-portfolio optimization with portfolio and marginal risk constraints," Annals of Operations Research, Springer, vol. 262(2), pages 547-578, March.
    12. Martin Branda & Max Bucher & Michal Červinka & Alexandra Schwartz, 2018. "Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization," Computational Optimization and Applications, Springer, vol. 70(2), pages 503-530, June.
    13. Zhang, Zhi-Hai & Unnikrishnan, Avinash, 2016. "A coordinated location-inventory problem in closed-loop supply chain," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 127-148.
    14. Xiaojin Zheng & Xiaoling Sun & Duan Li, 2014. "Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 690-703, November.
    15. Eduardo Bered Fernandes Vieira & Tiago Pascoal Filomena, 2020. "Liquidity Constraints for Portfolio Selection Based on Financial Volume," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 1055-1077, December.
    16. Massol, Olivier & Banal-Estañol, Albert, 2014. "Export diversification through resource-based industrialization: The case of natural gas," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1067-1082.
    17. Moarefdoost, M. Mohsen & Lamadrid, Alberto J. & Zuluaga, Luis F., 2016. "A robust model for the ramp-constrained economic dispatch problem with uncertain renewable energy," Energy Economics, Elsevier, vol. 56(C), pages 310-325.
    18. Liu, Kanglin & Zhang, Zhi-Hai, 2018. "Capacitated disassembly scheduling under stochastic yield and demand," European Journal of Operational Research, Elsevier, vol. 269(1), pages 244-257.
    19. Chien-Ming Chen & Joe Zhu, 2011. "Efficient Resource Allocation via Efficiency Bootstraps: An Application to R&D Project Budgeting," Operations Research, INFORMS, vol. 59(3), pages 729-741, June.
    20. Shijie Liu & Andrew Adams & Boulis M. Ibrahim, 2013. "Effects of Tax on Investment Portfolios and Financial Markets Under Mixed Integer Stochastic Programming," CFI Discussion Papers 1304, Centre for Finance and Investment, Heriot Watt University.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2311.08871. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.