From small markets to big markets

Volume 122 / 2020

Laurence Carassus, Miklós Rásonyi Banach Center Publications 122 (2020), 41-52 MSC: Primary 93E20, 91B70, 91B16; Secondary 91G10, 46B09. DOI: 10.4064/bc122-3


We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising expected utility in this setting. Besides establishing the existence of optimizers under weaker assumptions than previous papers, we go on studying the relationship between optimal investments in finite market segments and those in the whole market. We show that certain natural (but nontrivial) continuity rules hold: maximal satisfaction, reservation prices and (convex combinations of) optimizers computed in small markets converge to their respective counterparts in the big market.


  • Laurence CarassusLéonard de Vinci Pôle Universitaire
    Research Center
    92 916 Paris La Défense, France
  • Miklós RásonyiAlfréd Rényi Institute of Mathematics
    Budapest, Hungary

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