Pricing of contingent claims in large markets

Oleksii Mostovyi () and Pietro Siorpaes ()
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Oleksii Mostovyi: University of Connecticut
Pietro Siorpaes: Imperial College London

Finance and Stochastics, 2025, vol. 29, issue 1, No 5, 177-217

Abstract: Abstract We consider the problem of pricing in a large market, which arises as a limit of small markets within which there are finitely many traded assets. We show that this framework allows accommodating both marginal-utility-based prices (for stochastic utilities) and arbitrage-free prices. Adopting a stochastic integration theory with respect to a sequence of semimartingales, we introduce the notion of marginal-utility-based prices for the large (post-limit) market and establish their existence, uniqueness and relation to arbitrage-free prices. These results rely on a theorem of independent interest on utility maximisation with a random endowment in a large market that we state and prove first. Further, we provide approximation results for the marginal-utility-based and arbitrage-free prices in the large market by those in small markets. In particular, our framework allows pricing asymptotically replicable claims, where we also show consistency in the pricing methodologies and provide positive examples.

Keywords: Infinite-dimensional stochastic control; Large market; Indifference pricing; Fair pricing; Davis pricing; Utility-based pricing; Arbitrage-free pricing; Asymptotic replicability; Duality theory; Semimartingale; Incomplete market; 93E20; 91G10; 91G15; 60H30; 60H05 (search for similar items in EconPapers)
JEL-codes: C61 G11 G12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00780-024-00554-0

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