Recent posts:

• 25 Jun 2025 Options Pricing

  A European call option is a contract that provides its holder the right, but not the obligation, to buy a specific quantity of an underlying asset at a pre-specified strike price on a specified future date. Thus, if you believe that, say, crude oil will increase in price next summer, you can buy a call option from the seller. If the oil price next summer does skyrocket, you can exercise the option and buy the pre-specified amount at the strike price, which is lower than the actual one. If instead, the oil price plummets, you don't have to exercise the option. You'll only lose the price you paid for the option. So, effectively, by buying an option you are buying, literally, an option, an opportunity for a better transaction. Yet, even this opportunity has to have a market price, given that somebody is willing to sell it or buy it. What should it be? How are options priced?

  
  
• 18 Jun 2025 How To Intercept a Missile

  Today, missile guidance sits at the crossroads of classical control theory, real-time signal processing and modern AI-driven state estimation. Whether you’re tuning fins on a supersonic interceptor or programming a drone swarm to shadow evasive targets, the same principles of geometry, feedback and computational efficiency govern success under extreme time pressure. Let's explore the basics of this hugely important topic.

  
  
• 05 Jun 2025 Impulses, Feedback, Control

  Control engineering is a very useful topic for the real world. It is concerned with studying dynamic systems and figuring out how to control them in a way that is beneficial for us. I've encountered multiple references to it but have never studied it carefully. In autonomous driving, for example, it's common to predict a bunch of waypoints marking the intended future trajectory of the vehicle. You then give them to a PID controller that will try its best to follow that trajectory. But how does it work exactly? Well, I'm quite satisfied that I finally got to read up a bit on this topic. Because the principles of control theory are applicable in diverse contexts - reinforcement learning with known dynamics, economic policy design, digital filters for audio and image processing, everywhere really.

  
  
• 23 May 2025 The Price of Anarchy

  When it comes to economic calculation and scarce resource allocation, a capitalist decentralized system of decision-making is more efficient than a socialist centralized one. Why? Because a decentralized system breaks down the larger problem instance - e.g. resource allocation across a whole industry - into multiple smaller instances - allocation within a firm or a household - which are easier to solve. This approach of dividing the problem, solving the subproblems, and combining them, does not provide the best solution, but often is good enough. Here we're interested in quantifying this statement, at least for well-formalized simple problems. We'll build intuition about the behaviour of systems which when let alone evolve according to their selfish participants, and we'll compare them to their best possible outcomes.

  
  
• 14 May 2025 From Haggling to Algorithms

  A market is simply a place where people exchange things. Goods for money, promises for future goods, risks for security. But behind this simple act lies a sprawling architecture - an emergent machine of rules, signals, incentives, and delays. Why do prices fluctuate? How are trades matched? Who ensures that agreements are kept? These are not philosophical questions. They are mechanical ones. And like any complex mechanism, the financial market has evolved piece by piece, each part introduced to solve a problem, reduce friction, or create new possibility. What follows is a journey from barter to matching engines, from shouting traders to silent algorithms - an attempt to understand how markets for securities actually work. Not in metaphor, but in machinery.