Better Way to model Geometric Brownian Motion

Better Way to model Geometric Brownian Motion

In my last article, I introduced Geometric Brownian Motion and modeled the stochastic differential equation using the famous Monte Carlo Method. As I was not satisfied with the model and was looking at other approaches. Better Way to model Geometric Brownian Motion

In my last article, I introduced Geometric Brownian Motion and modeled the stochastic differential equation using the famous Monte Carlo Method. As I was not satisfied with the model and was looking at other approaches I finally stumbled upon Approximate Dynamic Programming.

We will use Approximate dynamic programming (also known as reinforcement learning) to model stochastic differential equation in these article( To learn dynamic programming you can go to MIT-OpenCourseWare, https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-231-dynamic-programming-and-stochastic-control-fall-2015/index.htm ). Our approach will be as follows:

This infinite dimensional stochastic optimization problem is temporally discretized by means of suitable discretizations of the underlying SDE and it is spatially discretized by means of fully connected deep artifcial neural network approximations. The resulting infinite dimensional stochastic optimization problem is then solved by means of stochastic gradient descent type optimization algorithms( Adam Optimizer). ( To understand the complete mathematics, https://arxiv.org/abs/1806.00421 )

We model on Python using tensorflow. First we build the base functions namely the neural network and the kolmogorov train and test algorithm. we employ a fully-connected feedforward neural network with one input layer, two hidden layers, and one one-dimensional output layer in our implementations in the case of each of these examples. We also use batch normalization just before the first linear transformation, just before each of the two nonlinear activation functions in front of the hidden layers as well as just after the last linear transformation.

tensorflow quantitative-finance stochastic-gradient python finance

Bootstrap 5 Complete Course with Examples

Bootstrap 5 Tutorial - Bootstrap 5 Crash Course for Beginners

Nest.JS Tutorial for Beginners

Hello Vue 3: A First Look at Vue 3 and the Composition API

Building a simple Applications with Vue 3

Deno Crash Course: Explore Deno and Create a full REST API with Deno

How to Build a Real-time Chat App with Deno and WebSockets

Convert HTML to Markdown Online

HTML entity encoder decoder Online

top 30 Python Tips and Tricks for Beginners

In this post, we'll learn top 30 Python Tips and Tricks for Beginners

Lambda, Map, Filter functions in python

You can learn how to use Lambda,Map,Filter function in python with Advance code examples. Please read this article

Python Tricks Every Developer Should Know

In this tutorial, you’re going to learn a variety of Python tricks that you can use to write your Python code in a more readable and efficient way like a pro.

How to Remove all Duplicate Files on your Drive via Python

Today you're going to learn how to use Python programming in a way that can ultimately save a lot of space on your drive by removing all the duplicates. We gonna use Python OS remove( ) method to remove the duplicates on our drive. Well, that's simple you just call remove ( ) with a parameter of the name of the file you wanna remove done.

Basic Data Types in Python | Python Web Development For Beginners

In the programming world, Data types play an important role. Each Variable is stored in different data types and responsible for various functions. Python had two different objects, and They are mutable and immutable objects.