Dynamic Approach for Financial Asset Price by Feynman –Kac Formula

Abstract

 This paper has obtains the partial differential equation that describes the expected price of a financial asset whose price is a stochastic process given by a stochastic differential equation. We tried finding the expected selling price of an asset and exiting time by using of Feynman –Kac Formula. We assume that the asset is sold at the moment when its price rises above or falls below a certain limit, and thus the solution v has to satisfy x - v = 0 at the boundary points x. The expected selling price depends nearly linearly on the price at time t, and also weakly on t and the expected payoff of an asset for which a limit sales order has been placed and the same asset without sales order over a time span T, as a function of t