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No free lunch for markets with multiple numéraires

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  • Carassus, Laurence

Abstract

We consider a new framework, that of a global market with a finite number of submarkets, where there is a tradable numéraire for each submarket, but no tradable numéraire for the global market. Under a global no arbitrage condition, we show the existence of a common density from which equivalent (local) martingale measures are constructed for each submarket. We also introduce several superreplication prices, depending on the chosen type of hedging: on the global market, on a given submarket or on all submarkets separably. We prove duality results on these prices that allow to assess differences in characteristics between the submarkets, such as liquidity or credit quality. The results are applied in concrete situations, in particular in a Brownian setup.

Suggested Citation

  • Carassus, Laurence, 2023. "No free lunch for markets with multiple numéraires," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    • Handle: RePEc:eee:mateco:v:104:y:2023:i:c:s0304406822001318
    DOI: 10.1016/j.jmateco.2022.102805
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    References listed on IDEAS

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