Path integral method for stochastic equations of financial engineering

: pp. 166–177
Received: August 13, 2021
Accepted: January 19, 2022

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