Generalized measure Black-Scholes equation: Towards option self-similar pricing
In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the pointwise option price dynamics depends on a measure representing the investors' 'uncertainty'. We make use of the theory of non-symmetric Dirichlet forms and the abstract theory of partial differential equations to establish well posedness of the problem. A detailed numerical analysis is given in the case of self-similar measures.
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