A Stochastic Algorithm and Multiple Scale for Solution to PDE With Financial Application

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Abstract: This paper presents an application of multiple scale and stochastic approximation method to discretize generic financial PDE. The multiple scale method was adopted in calculating the periodic solution resulted from a Hopf bifurcation of a discretized generic PDE to monitor and stabilize the oscillatory movement of the market price of stock, thereafter a stochastic algorithm was formulated to price an American option under the Black-Scholes model through a drifted financial derivative system. With finer discretization, positive periodic solution, space nodes and time nodes, we demonstrate that the drifted financial derivative system can be efficiently and easily solved with high accuracy, by using a stochastic approximation method which proves to be faster in pricing an American options. An illustrative example is given in a concrete setting.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 16, 2017, Art. #10

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Bright O. Osu, Okechukwu U. Solomon, "A Stochastic Algorithm and Multiple Scale for Solution to PDE With Financial Application," WSEAS Transactions on Mathematics, vol. 16, pp. 74-83, 2017, DOI:
Bright O. Osu, Okechukwu U. Solomon. A Stochastic Algorithm and Multiple Scale for Solution to PDE With Financial Application. WSEAS Transactions on Mathematics. 2017;16:74-83.
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