Abstract
The objective of this paper is to provide an analytic theory for pricing path-dependent options of European type. General conditions for the path-dependencies are introduced, which allow a wide range of application. We present a partial differential equation describing the fair price process of a path-dependent option in a Black---Scholes world, where the classical Black---Scholes equation involves additional terms caused by the path-dependency of the option. The main result is that the problem is well posed in appropriate function spaces.
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