optimization

In 2014, Ian Goodfellow, then at OpenAI, published his seminal paper, titled “Generative Adversarial Networks”1, detailing how competition between generator and discriminator functions, approximated by neural networks, can train the generator to produce realistic images. In this article I will be discussing the theory behind this idea, my own implementation in Julia (mirroring the network structure in Goodfellow’s original paper), and show some of the images I was able to get out....

The development of mathematical finance, much like the processes it aims to study, has had a particularly jumpy history. A major leap came in 1973, when the Black-Scholes option pricing model was published and mathematically understood. The essential idea is to model the underlying asset $S_t$ of an option as a geometric brownian motion, with a stochastic differential equation (SDE), given by $$ dS_t = \mu S_t \ dt + \sigma S_t \ dW_t, $$...