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A Short Note on Super-Hedging an Arbitrary Number of European Options with Integer-Valued Strategies

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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 are not 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 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.

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Authors and Affiliations

  1. Faculty of Sciences of Tunis, Tunis, Tunisia

    Dorsaf Cherif & Meriam El Mansour

  2. Ceremade, UMR CNRS 7534, Paris-Dauphine University, PSL, Place du Maréchal De Lattre De Tassigny, 75775, Paris cedex 16, France

    Meriam El Mansour & Emmanuel Lepinette

Authors
  1. Dorsaf Cherif
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  2. Meriam El Mansour
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  3. Emmanuel Lepinette
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Correspondence to Emmanuel Lepinette.

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Communicated by Klaus Reiner Schenk-Hoppe.

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Cherif, D., El Mansour, M. & Lepinette, E. A Short Note on Super-Hedging an Arbitrary Number of European Options with Integer-Valued Strategies. J Optim Theory Appl 201, 1301–1312 (2024). https://doi.org/10.1007/s10957-024-02409-2

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  • DOI: https://doi.org/10.1007/s10957-024-02409-2

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