Quantum Finance: Path Integrals And Hamiltonian... Apr 2026

: The classical Black-Scholes equation for option pricing can be recast as a Schrödinger-like equation using a non-Hermitian Hamiltonian.

This approach provides a powerful alternative to traditional stochastic calculus by reformulating financial evolution as the motion of states in a linear vector space. 1. The Hamiltonian in Finance The Hamiltonian ( Quantum Finance: Path Integrals and Hamiltonian...

Feynman path integrals offer a method to calculate the probability of asset price transitions by summing over all possible price trajectories. PATH INTEGRALS AND HAMILTONIANS : The classical Black-Scholes equation for option pricing

) serves as the generator of time evolution for financial instruments. The Hamiltonian in Finance The Hamiltonian ( Feynman

: In this framework, financial securities are described as elements in a linear vector state space, where the Hamiltonian operator determines how these states change over time.

: The Hamiltonian formulation allows for the use of "financial potentials" to model market conditions and "eigenfunctions" to find exact solutions for various path-dependent options. 2. Path Integrals and Asset Pricing

Quantum finance utilizes the mathematical frameworks of quantum mechanics—specifically and Feynman path integrals —to model complex financial systems like option pricing and interest rate dynamics.