Welcome to my current algorithms development page. Here I will discuss some projects I am currently interested in. I am interested in several areas of mathematics: Finance, Physics, Machine learning and Asymptotic Analysis. 

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Intro: What is it that people in the finance industry are so interested in? One topic of interest is fair pricing of items. One can price items by "feel" or attempt to determine fair prices mathematically. The mathematics used to determine fair prices can be quite complex and require knowledge of Stochastic Differential Equations (SDE), Partial Differential Equations (PDE), Statistics and more. 

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For example, setting prices on options with many (potentially correlated) underlyings require one to solve a high-dimensional Black-Scholes equation. Of course the Black-Scholes equation comes with its own simplifying assumptions. For example, it does not tell you how to deal with "Fat tails" or non-log normal returns.

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The world is highly non-linear thus discovering its patterns could be limited to data driven methods such as machine learning. Not only can machine learning do this, but it can also help improve current algorithms. For example, conventionally, the high dimensional Black-Scholes PDE is solved using Monte-Carlo integration. However, it has been shown that machine learning can also efficiently solve high-dimensional PDEs. This implies an interesting future research direction as there are many ways to structure a neural network.

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These issues and more is what I am currently exploring. I will provide a growing list of topics that I am currently working. As this section is an on going project, many developments are currently incomplete. I will try to post the date of last update for each of these projects.

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