Articlehybrid2018

Arbitrage-free pricing of derivatives in nonlinear market models

Tomasz R. Bielecki · Igor Cialenco · Marek Rutkowski

19 citations0/0 files storedProbability Uncertainty and Quantitative Risk

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

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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References

1997Backward Stochastic Differential Equations in Finance 2005The Mathematics of Arbitrage 2007The numéraire portfolio in semimartingale financial models 1996On the pricing of contingent claims under constraints 2006The Mathematics of Arbitrage 2010Partial Differential Equation Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs 2012BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS—PART II: CVA 2013BSDEs with jumps, optimization and applications to dynamic risk measures

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