Path integral method for stochastic equations of financial engineering

: pp. 166–177
Received: August 13, 2021
Accepted: January 19, 2022
Lviv Polytechnic National University
Lviv Polytechnic National University

The integral path method was applied to determine certain stochastic variables which occur in problems of financial engineering.  A stochastic variable was defined by a stochastic equation where drift and volatility are functions of a stochastic variable.  As a result, for transition probability density, a path integral was built by substituting variables Wiener's path integral (Wiener's measure).  For the stochastic equation, Ito rule was applied in order to interpret a stochastic integral.  The path integral for transition probability density was also found as a result of the Fokker--Planck equation solution, corresponding to the stochastic equation.  It was shown that these two approaches give equivalent results.

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Mathematical Modeling and Computing, Vol. 9, No. 1, pp. 166–177 (2022)