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Orders of Magnitude of Probabilities
Introduction We, humans, live in the world of common events. The majority of events we observe on a day-to-day basis are familiar, meaning they are common enough that we don’t bother to notice them. We rarely see unfamiliar events; they are usually rare (for us). This is why humans are...
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The Maker-Taker Coin Game: A Statistical Look at Prediction Market Pricing Part 1
Maker-Taker Coin Game
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Chapter 2: Permutations and Symmetry
In the first chapter, we embarked on an exploratory journey into the world of stochastic calculus, starting with the basic yet profound concept of the random walk. We began by demystifying the complexity of probability theory, revealing its inherent beauty and simplicity through the lens of discrete-time random walks. We...
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Chapter 1: Introduction to Random Walk
The initial encounter with stochastic calculus can be challenging, often appearing intricate and difficult to comprehend. This complexity can be attributed to certain prerequisites assumed by many introductory materials in the field. My goal here is to revisit this topic, starting from a foundational level accessible to those new to...
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Multi-Arm Bandits for Recommendation Systems
Envision yourself as a store owner looking to boost foot traffic. You hatch a plan: stand at the front and actively promote your items to those walking by. With enthusiasm, you quickly wear a striking outfit and hold up a blank board, ready to publicize a special deal. However, when...
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Optimizing Risks for a Portfolio of Cryptocurrencies
Created together with Maxim Korotkov and Dmytro Karabash Image credit geralt at pixabay In this post we will talk about optimizing a simple portfolio of cryptocurrency. The approaches below have been successfully applied to stock options trading and, as we see, work quite well for crypto. Also, crypto is great to...
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Volatility Estimation Using MCMC
[mathjax] Problem In the financial world, it is often can be found examples of the application of the modeling price return distribution with an assumption of its normality. Applying the normal distribution in the price simulation makes the model relatively simple and computational chip. It also a very convenient solution...