Discrete versus continuous time models: Local martingales and singular processes in asset pricing theory

Robert Jarrow () and Philip Protter

Finance Research Letters, 2012, vol. 9, issue 2, 58-62

Abstract: In economic theory, both discrete and continuous time models are commonly believed to be equivalent in the sense that one can always be used to approximate the other, or equivalently, any phenomena present in one is also present in the other. This common belief is misguided. Both (strict) local martingales and singular processes exist in continuous time, but not in discrete time models. More importantly, their existence reflects real economic phenomena related to arbitrage opportunities, large traders, asset price bubbles, and market efficiency. And as an approximation to trading opportunities in real markets, continuous trading provides a better fit and should be the preferred modeling approach for asset pricing theory.

Keywords: Local martingales; Singular processes; Arbitrage opportunities; Large traders; Asset price bubbles; Market efficiency (search for similar items in EconPapers)
JEL-codes: G10 G12 G13 G14 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:finlet:v:9:y:2012:i:2:p:58-62

DOI: 10.1016/j.frl.2012.03.002

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