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We consider the stochastic functional differential equations with finite delay driven by G-Brownian motion. Under the global Carathéodory conditions we prove the existence and uniqueness, and as an application, we price the European call option when the underlying asset's price follows such an equation

abstract and applied analysis

Successive Approximation of SFDEs with Finite Delay Driven by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>-Brownian Motion

Successive Approximation of SFDEs with Finite Delay Driven byG-Brownian Motion