Optional projection under equivalent local martingale measures

Francesca Biagini (), Andrea Mazzon and Ari-Pekka Perkkiö
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Francesca Biagini: Ludwig-Maximilians Universität
Andrea Mazzon: Ludwig-Maximilians Universität
Ari-Pekka Perkkiö: Ludwig-Maximilians Universität

Finance and Stochastics, 2023, vol. 27, issue 2, No 5, 435-465

Abstract: Abstract We study optional projections of G ${\mathbb{G}}$ -adapted strict local martingales on a smaller filtration F ${\mathbb{F}}$ under changes of equivalent martingale measures. General results are provided as well as a detailed analysis of two specific examples given by the inverse Bessel process and a class of stochastic volatility models. This analysis contributes to clarify the absence of arbitrage opportunities of market models under restricted information.

Keywords: Local martingale; Optional projection; Local martingale measure; Filtration shrinkage; 60G07; 60H30; 60G44 (search for similar items in EconPapers)
JEL-codes: C65 D82 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00780-023-00503-3

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