A system of non-local parabolic PDE and application to option pricing |
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Authors: | Anindya Goswami Jeeten Patel Poorva Shevgaonkar |
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Institution: | 1. Mathematics Department, IISER, Pune, Indiaanindya@iiserpune.ac.in;3. Mathematics Department, IISER, Pune, India;4. Mathematics Department, IIT, Kharagpur, India |
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Abstract: | This article includes a proof of well posedness of an initial-boundary value problem involving a system of non-local parabolic partial differential equation (PDE), which naturally arises in the study of derivative pricing in a generalized market model, which is known as a semi-Markov modulated geometric Brownian motion (GBM) model We study the well posedness of the problem via a Volterra integral equation of second kind. A probabilistic approach, in particular the method of conditioning on stopping times is used for showing the uniqueness. |
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Keywords: | Semi-Markov processes Volterra integral equation non-local parabolic PDE locally risk minimizing pricing optimal hedging |
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