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Replication and shortfall risk in a binomial model with transaction costs

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Abstract

The shortfall risk is defined as the optimal mean value of the terminal deficit produced by a self-financing portfolio whose initial value is smaller than what is required to replicate a contingent claim. In this paper we look for an explicit expression for it, as well as for the optimal strategy, when the market model is a binomial model with proportional transaction costs. We first study replication of European claims which satisfy suitable assumptions. We then investigate the shortfall minimization problem in a framework very similar to that without transaction costs.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Barbara Trivellato

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  1. Barbara Trivellato
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Correspondence to Barbara Trivellato.

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The author thanks the referee for useful comments on an earlier version of the present paper.

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Trivellato, B. Replication and shortfall risk in a binomial model with transaction costs. Math Meth Oper Res 69, 1–26 (2009). https://doi.org/10.1007/s00186-007-0208-3

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  • DOI: https://doi.org/10.1007/s00186-007-0208-3

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