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Hedging, Pareto Optimality, and Good Deals

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Abstract

In this paper, we will describe a framework that allows us to connect the problem of hedging a portfolio in finance to the existence of Pareto optimal allocations in economics. We will show that the solvability of both problems is equivalent to the No Good Deals assumption. We will then analyze the case of co-monotone additive monetary utility functions and risk measures.

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Notes

  1. In order to distinguish between two senses of arbitrage, we will henceforth refer to them as economic and financial arbitrage.

  2. For p<∞, B ∗ is isomorphic to the topological dual of B. For p=∞, B ∗ is the dual of B when the former is considered with the weak-star topology.

  3. http://www.dbresearch.com/servlet/reweb2.ReWEB?rwnode=DBR_INTERNET_EN-PROD$EM&rwobj=CDS.calias&rwsite=DBR_INTERNET_EN-PROD.

  4. Of course it should be modified by CDS spread, however, the result is still very small number.

  5. The internal access to AIG assessment of probability of default is impossible, made us to speculate this probability.

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Authors and Affiliations

  1. Department of Economics, Concordia University, 1455 de Maisonneuve Blvd. West, H 1155, Montreal, Quebec, H3G 1M8, Canada

    Hirbod Assa

  2. Department of Mathematics, Jacobs University, Campus Ring I Jacobs University, 28759, Bremen, Germany

    Keivan Mallahi Karai

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  1. Hirbod Assa
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  2. Keivan Mallahi Karai
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Correspondence to Hirbod Assa.

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Assa, H., Karai, K.M. Hedging, Pareto Optimality, and Good Deals. J Optim Theory Appl 157, 900–917 (2013). https://doi.org/10.1007/s10957-012-0209-0

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