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
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. Quantum Finance: Path Integrals and Hamiltonian...
: 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 Feynman path integrals offer a method to calculate
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 ( The Hamiltonian in Finance The Hamiltonian ( :
: The classical Black-Scholes equation for option pricing can be recast as a Schrödinger-like equation using a non-Hermitian Hamiltonian.
) serves as the generator of time evolution for financial instruments.
: 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.