Existence of a fundamental solution of partial differential equations associated to Asian options |
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Affiliation: | 1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India;2. Department of Mathematics, University of North Bengal, Darjeeling 734013, India;3. Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India |
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Abstract: | We prove the existence and uniqueness of the fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in the Black & Scholes setting for the pricing problem relevant to path dependent options. We improve previous results in that we provide a closed form expression for the solution of the Cauchy problem under weak regularity assumptions on the coefficients of the differential operator. Our method is based on a limiting procedure, whose convergence relies on some barrier arguments and uniform a priori estimates recently discovered. |
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Keywords: | Partial differential equations Option pricing Kolmogorov operator |
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