Simulating the Geometric Brownian Motion. We discuss Random Walk, Wiener Processes and the Black-Scholes-Merton model. Geometric Brownian Motion (GBM) is an ubiquitous random process, used not only in science, but also in finance, for example in the Black-Scholes model. The main ingredient of such mathematical object is the Brownian Motion, a continuous-time random process that can be thought of as the limit of a Random Walk...
An introduction to the world of Support Vector Machines. We discuss how SVM's classify objects. Includes A C# Accord-Framework example. Consider a set of points which constitute our observations or test set. These points are labeled as either +1 or -1. If we had a new observation, 1) how would we classify it? Should we label the new point as +1 or as -1? 2) How to quantify the confidence we have that the point belongs to that class? This is a Classification Problem. The problem consist in "learning" the mapping $$f(\mathbf{x}_i,\alpha_i):\mathbf{x}_i\mapsto y_i$$Read more...
Support Vector Machines and some of its mathematical aspects. We discuss Classification, Reproducing Kernel Hilbert Spaces and more. In a classification problem we want to classify or label a new observation, having trained our model with a set of observations whose class is known. One approach is to think that all elements that belong to the same class are *similar* in some way. We thus need a concept of similarity or distance...