Over-the-counter (OTC) in finance refers to the process of trading financial instruments directly between two parties without a central exchange or broker. OTC trading can involve various assets, including stocks, bonds, commodities, and derivatives. Key characteristics of OTC trading include: 1. **Decentralization**: Unlike exchange-traded securities, OTC securities are not listed on formal exchanges like the New York Stock Exchange (NYSE) or NASDAQ. Trades are executed directly between parties, often facilitated by dealers.

Optimal stopping is a decision-making problem in probability theory and statistics, where one must decide the best time to take a particular action in order to maximize an expected reward or minimize a cost. The key challenge in optimal stopping is that the decision-maker often does not know the future values of the processes involved, making it necessary to make choices based on partial information.

Time-weighted return (TWR) is a method of measuring the performance of an investment portfolio that eliminates the impact of cash flows (deposits and withdrawals) made during the investment period. This makes it particularly useful for evaluating the performance of an investment manager, as it reflects the manager's ability to generate returns independent of the timing of cash flows. The time-weighted return is calculated by breaking down the investment period into sub-periods, typically corresponding to the dates when cash flows occur.

Kill stealing, often abbreviated as "ks," is a term commonly used in multiplayer online games, particularly in role-playing games (RPGs) and first-person shooters (FPS). It refers to the act of a player dealing the final blow to an enemy or monster that another player was already fighting or had significantly weakened. This can lead to frustration, as it deprives the original player of the kill, its associated rewards (like experience points or loot), and can potentially disrupt teamwork.

Realized variance is a statistical measure used to quantify the variability of asset returns over a specified period, typically applied in the context of financial markets. It is calculated by using high-frequency data, such as minute-by-minute or daily returns, to provide a more accurate estimate of the variance of an asset's returns.

In economics, "regular distribution" isn't a commonly used term like "normal distribution" or "log-normal distribution," which refer to specific statistical distributions used to model data in various contexts. However, it may refer to the general concept of "regular" in the context of how resources, income, or wealth are distributed among individuals or groups in an economy. Often, regular distribution may be sought in discussions about equity and fairness in economic systems.

A **self-financing portfolio** is a concept in finance and investment that refers to a portfolio of assets in which any changes in the portfolio's composition are financed entirely through the portfolio's own changes in value, rather than through external cash flows (such as additional investments or withdrawals). In other words, a self-financing portfolio does not require any external funding to maintain or adjust its positions.

The shadow rate is a concept used in economics and finance to describe an implicit interest rate that reflects the monetary policy stance when traditional policy tools, like the nominal interest rate, reach their lower bound (often close to zero). In such situations, central banks may find it challenging to stimulate the economy solely through standard interest rate adjustments, leading to the implementation of unconventional monetary policies, such as quantitative easing or forward guidance.

A short-rate model is a type of interest rate model used primarily in finance to describe the evolution of interest rates over time. In these models, the "short rate" refers to the interest rate for a very short time period, typically treated as a single period (like one day) or the instantaneous interest rate. The key feature of short-rate models is that they focus on modeling this single rate rather than the entire yield curve or longer-term rates directly.

Mathematical puzzles are problems or riddles that require mathematical reasoning, logic, and often creative thinking to solve. They can range from simple arithmetic questions to complex problems involving advanced concepts in mathematics. Mathematical puzzles are designed to challenge the solver and can often be solved using various techniques and approaches, including algebra, geometry, number theory, combinatorics, and more.

Dots and Boxes is a classic pencil-and-paper game typically played by two players. The game involves a grid of dots, where players take turns drawing horizontal or vertical lines between adjacent dots. The objective of the game is to complete as many squares (boxes) as possible. ### Rules: 1. **Setup**: Start with an empty grid of dots. The size of the grid can vary, but a common choice is 4x4 or 5x5 dots.

Spoof is a party game that involves players trying to outsmart each other by imitating or creating fake versions of things, typically involving clues or deception. The exact mechanics can vary depending on the specific version of the game, but it often includes elements of guessing and bluffing. In typical Spoof gameplay, players may take turns presenting a scenario, statement, or clue, and the other players must discern whether it is true or false, or who is the best at mimicking something.

A Tetromino is a geometric shape composed of four squares connected edge to edge. It is commonly associated with the classic video game Tetris, where players rotate and position these shapes to complete horizontal lines, which then disappear and earn points.

Fay's trisecant identity is an important result in the theory of elliptic functions and algebraic geometry. It expresses a certain relationship among elliptic functions and their derivatives. In particular, Fay's trisecant identity concerns the trisecant curves associated with an elliptic curve. The identity can be stated in terms of a given elliptic function \( \wp(z) \), which is related to the Weierstrass elliptic functions.

Hermite's identity is a result in number theory related to the representation of integers as sums of distinct squares or as sums of two squares.

The Hamilton Institute is a research institute based in Ireland, focused on the fields of mathematical sciences and statistical sciences. It was established to foster research and education in the areas of applied and computational mathematics, as well as statistical methodology. The institute is often associated with the promotion of interdisciplinary research, combining various fields such as mathematics, engineering, computer science, and the social sciences.

Liouville's formula is a significant result in the theory of differential equations, particularly in the context of linear ordinary differential equations. It describes the behavior of the Wronskian determinant of a system of linear ordinary differential equations.

International research institutes for mathematics refer to organizations and facilities dedicated to advancing the field of mathematics through research, collaboration, and education. These institutions often bring together mathematicians from around the world to collaborate on various mathematical problems, conduct research, and promote the dissemination of mathematical knowledge. Some notable examples of international research institutes for mathematics include: 1. **Institute for Advanced Study (IAS)** in Princeton, New Jersey, USA - A prestigious research institute that has hosted many of the world's leading mathematicians.

The Abdus Salam School of Mathematical Sciences (ASSMS) is an academic institution in Pakistan, established in honor of the renowned Pakistani theoretical physicist Abdus Salam, who won the Nobel Prize in Physics in 1979. The school is located in the city of Lahore and is part of the Government of Punjab's initiative to promote advanced education and research in mathematics and related fields.