  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.
