Some Financial Problems Based On Quantum Information And Quantum Stochastic Calculus

The application of quantum mechanics in financial problems has been intensively studied in recent years.In this dissertation,we present the quantum model of three-dimensional discrete space based on the Schrodinger equation and the Fourier transform.At the same time,we obtain the price changes and stock return in equilibrium of stock market.The paper is organized as follows:In Chapter 1,we briefly describe the background and the current situation concerning our research topics.In addition,we introduce some general.concepts and fundamental knowledge of quantum finance.In Chapter 2,we study the space-inhomogeneous three-state quantum walks on the line,a one-phase model and a two-phase model included.By using the reduced matrix method introduced by Konno et al,we calculate their eigenvalues and get corresponding stationary measure.In Chapter 3,we research the European option pricing model based on the nonlinear Schrodinger equation with external potential field and obtain its periodic solution.By taking advantage of the Runge-Kutta algorithm,we discuss the discrete boundary value problem.In Chapter 4,in order to describe the quantum model of stock market,we es-tablish the quantum model of three-dimensional discrete space based on the Fourier transform and the Schrodinger equation.Moreover,we study the stock return in equilibrium of stock market by Gaussian function.