# 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.

## top 30 Python Tips and Tricks for Beginners

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