Related papers: Phynance
This article contains the lecture notes for the short course ``Introduction to Econophysics,'' delivered at the II Brazilian School on Statistical Mechanics, held in Sao Carlos, Brazil, in February 2004. The main goal of the present notes…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
Using fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued H\"{o}lder continuous functions of order $\displaystyle \beta \in (\frac13, \frac12)$ and $f$ is a continuously…
In this note we review the basic mathematical ideas used in finance in the language of modern physics. We focus on discrete time formalism, derive path integral and Green's function formulas for pricing. We also discuss various risk…
The book deals with a stochastic formulation of path integration in real time, by rotating the_space_ variables over exp(i pi/4). Preliminary chapters deal with quantum and classical mechanics, probability theory and stochastic calculus,…
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on…
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
In this paper we show the existence and form uniqueness of a solution for multidimensional backward stochastic differential equations driven by a multidimensional L\'{e}vy process with moments of all orders. The results are important from a…
These are course notes on the application of SDEs to options pricing. The author was partially supported by NSF grant DMS-0739195.
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
The price of a financial derivative can be expressed as an iterated conditional expectation, where the inner term conditions on the future of an auxiliary process. We show that this inner conditional expectation solves an SPDE (a…
We apply a physics-informed deep-learning approach the PINN approach to the Black-Scholes equation for pricing American and European options. We test our approach on both simulated as well as real market data, compare it to…
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…
Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view.…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…