Arbitrage-free pricing of derivatives in nonlinear market models

Tomasz R. Bielecki; Igor Cialenco; Marek Rutkowski

doi:10.1186/s41546-018-0027-x

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2018, Volume 3: 2. Doi: 10.1186/s41546-018-0027-x

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Arbitrage-free pricing of derivatives in nonlinear market models

1. Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616, IL, USA;
2. School of Mathematics and Statistics, University of Sydney, Sydney 2006, NSW, Australia;
3. Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661 Warszawa, Poland

Received: January 28, 2017

Revised: March 14, 2018

Published: September 2020

The research of I. Cialenco and M. Rutkowski was supported by the DVC Research Bridging Support Grant BSDEs Approach to Models with Funding Costs. Part of the research was completed while I. Cialenco and M. Rutkowski were visiting the Institute for Pure and Applied Mathematics (IPAM) at UCLA, which is funded by the National Science Foundation. We would also like to thank the anonymous referees and Stéphane Crépey for their insightful and helpful comments and suggestions, which helped us greatly to improve the final manuscript.

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Abstract

The objective of this paper is to provide a comprehensive study of the no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affecting the trading mechanism, such as collateralization and capital requirements. To achieve our goals, we extend in several respects the nonlinear pricing approach developed in (El Karoui and Quenez 1997) and (El Karoui et al. 1997), which was subsequently continued in (Bielecki and Rutkowski 2015).

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Mathematics Subject Classification: 91G40;60J28.

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