Amwoga KhalwaleLinear Programming (LP): LP problems have an objective and all constraints that are linear functions of the decision variables. LP problems are intrinsically easier to solve than general nonlinear problems, as they have at most one feasible region with “flat faces” on its outer surface, and the optimal solution will always be found at a … Read more
The Central Limit Theorem states that, given certain conditions, the distribution of the mean of a large sample of independent and identically distributed (i.i.d.) random variables will approximate a normal distribution, even if the original variables are not normally distributed. In other words, as the sample size (n) increases, the distribution of the sample mean … Read more
The Singular Value Decomposition (SVD) is a factorization of a matrix A into three matrices: The SVD can be written as: A = U Σ V* The singular values in Σ are non-negative and represent the importance of each column of A. The columns of U and V are orthonormal, meaning they have length 1 … Read more
David X. Li, a Chinese-born Canadian quantitative analyst and actuary, introduced the Gaussian copula function in his 2000 paper “On Default Correlation: A Copula Function Approach”. The paper aimed to provide a mathematical framework for modeling default correlations between multiple credit instruments, such as collateralized debt obligations (CDOs). Enter Li, a star mathematician who grew up … Read more
A Gaussian Process (GP) is a statistical model, or more precisely, it is a stochastic process. There are two ways I like to think about GPs, both of which are highly useful. What we can do with GPs is absolutely amazing. Basically, they are an extremely flexible tool for modelling functions. They are completely specified … Read more
A cubic Bézier curve, commonly used in computer graphics to model smooth curves. Adapting it as an indicator for predicting stock price movements involves translating the concept into a financial context. The Bézier curve equation: b(t) = (1-t)³ * p0 + 3*(1-t)²t * p1 + 3(1-t)*t² * p2 + t³ * p3 where: In a … Read more
Hedge funds and mutual funds are both types of investment vehicles that pool money from investors to buy securities like stocks, bonds, or other assets. Regulation and Structure Mutual Funds Hedge Funds Investment Strategies Mutual Funds Hedge Funds Fees Mutual Funds Hedge Funds Liquidity and Redemption Mutual Funds Hedge Funds Performance and Risk Mutual Funds … Read more
Volume Profile and Market Profile are invaluable analytical tools for traders, credited to Mr. Peter J. Steidlmayer. These tools help traders inspect market structures to identify trading opportunities. Volume Profile is a visual representation of trading volume at various price levels within a specified time frame. It illustrates where the most substantial trading activity has … Read more
Choosing between futures and forex trading depends on several factors, including your trading goals, risk tolerance, market knowledge, and the specific characteristics of each market. Futures Trading: Advantages Disadvantages Forex Trading: Advantages Disadvantages Which is Better? Conclusion
Laboratory apparatus refers to the various tools, equipment, and devices used by scientists, researchers, and students in laboratories to perform experiments, analyze data, and conduct research across various scientific disciplines. Importance of Laboratory Apparatus Types of Laboratory Apparatus Measuring Tools Heating Equipment Mixing and Stirring Tools Holding and Handling Filtration and Separation Reaction Vessels Analytical … Read more