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Pricing of contingent claims in large markets

Author

Listed:
  • Oleksii Mostovyi

    (University of Connecticut)

  • Pietro Siorpaes

    (Imperial College London)

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.

Suggested Citation

  • Oleksii Mostovyi & Pietro Siorpaes, 2025. "Pricing of contingent claims in large markets," Finance and Stochastics, Springer, vol. 29(1), pages 177-217, January.
    • Handle: RePEc:spr:finsto:v:29:y:2025:i:1:d:10.1007_s00780-024-00554-0
    DOI: 10.1007/s00780-024-00554-0
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    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;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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