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Existence of solutions of some boundary value problems with stochastic volatility
B O Osu1, E O Eze1, U E Obasi1
1Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.
Abstract:
This paper aims at obtaining the analytical solutions of some boundary value problems garnished with stochastic volatility, price volatility risk and the risk premium. A set of functions is constructed which transforms the problem into a Laplace equation and a heat equation. The analytical solutions of these equations are obtained. Then existence of a unique solution is achieved which represents the behavior of volatile behavior of the system. Some numerical illustration of the models is obtained using the Maple software.
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