In portfolio theory, a mutual fund separation theorem, mutual fund theorem, or separation theorem is a theorem stating that, under certain conditions, any investor's optimal portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the number of mutual funds is smaller than the number of individual assets in the portfolio. Here a mutual fund refers to any specified benchmark portfolio of the available assets. There are two advantages of having a mutual fund theorem. First, if the relevant conditions are met, it may be easier (or lower in transactions costs) for an investor to purchase a smaller number of mutual funds than to purchase a larger number of assets individually. Second, from a theoretical and empirical standpoint, if it can be assumed that the relevant conditions are indeed satisfied, then implications for the functioning of asset markets can be derived and tested. (Wikipedia).
Differential Equations: Separation of Variables
This video provides several examples of how to solve a DE using the technique of separation of variables. website: http://mathispower4u.com blog: http://mathispower4u.wordpress.com
From playlist First Order Differential Equations: Separation of Variables
Product Rule (1 of 2: It's Complicated...)
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From playlist Introduction to Differentiation
Here I show that the ratio of two continuous functions is continuous. I do it both by using epsilon-delta and the sequence definition of continuity. Interestingly, the proof is similar to the proof of the quotient rule for derivatives. Enjoy! Reciprocals of limits: https://youtu.be/eRs84C
From playlist Limits and Continuity
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
The Product Rule of Differentiation (Introduction)
This video is a new version of the introductory video to the product rule of differentiation. Site: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Differentiation Using the Product Rule
Ex 1: Chain Rule Concept Check
This example explains the proper use of the chain rule of differentiation using composite function notation to find a derivative function value. Site: http://mathispower4u.yolasite.com Blog: http://mathispower4u.wordpress.com
From playlist Differentiation Using the Chain Rule
Proof - The Chain Rule of Differentiation
This video proves the chain rule of differentiation. http://mathispower4u.com
From playlist Calculus Proofs
23. The Mutual Fund Theorem and Covariance Pricing Theorems
Financial Theory (ECON 251) This lecture continues the analysis of the Capital Asset Pricing Model, building up to two key results. One, the Mutual Fund Theorem proved by Tobin, describes the optimal portfolios for agents in the economy. It turns out that every investor should try to m
From playlist Financial Theory with John Geanakoplos
Learn to determine the points where a function is non differentiable
👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative exists at each point in its domain. To check the differentiability of a function, we first check that the function is continuous at every point in the domain. A function
From playlist Find the Differentiability of a Function
4. Portfolio Diversification and Supporting Financial Institutions
Financial Markets (2011) (ECON 252) In this lecture, Professor Shiller introduces mean-variance portfolio analysis, as originally outlined by Harry Markowitz, and the capital asset pricing model (CAPM) that has been the cornerstone of modern financial theory. Professor Shiller commences
From playlist Financial Markets (2011) with Robert Shiller
5. Insurance: The Archetypal Risk Management Institution
Financial Markets (ECON 252) Insurance provides significant risk management to a broad public, and is an essential tool for promoting human welfare. By pooling large numbers of independent or low-correlated risks, insurance providers can minimize overall risk. The risk management is tai
From playlist Financial Markets (2008) with Robert Shiller
Level 1 Chartered Financial Analyst (CFA ®): Sampling and Estimation
In this video, I'm looking forward to sharing highlights with you from the CFA section, sampling and estimation. Sampling and estimation in statistics are theoretically essential and foundational, but in actual practice, it's very important. This is the practice of using samples to draw in
From playlist Level 1 Chartered Financial Analyst (CFA ®) Volume 1
Take the derivative from the difference quotient without simplifying
👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
From playlist Evaluate the Limit (PC)
18. Professional Money Managers and Their Influence
Financial Markets (ECON 252) Most people are not very good at dealing in financial markets. Professional money managers, such as financial advisors and financial planners, assist individuals in matters of personal finance. FINRA and the SEC monitor the activities of these managers in or
From playlist Financial Markets (2008) with Robert Shiller
What is quantum mechanics? A minimal formulation (Seminar) by Pierre Hohenberg
29 December 2017 VENUE : Ramanujan Lecture Hall, ICTS , Bangalore This talk asks why the interpretation of quantum mechanics, in contrast to classical mechanics is still a subject of controversy, and presents a 'minimal formulation' modeled on a formulation of classical mechanics. In bot
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
Perspectives on Social Phenomena in Online Networks
(February 16, 2011) Jon Kleinberg focuses his discussion on issues that come up when thinking about social phenomenon on the web and some how it interacts with some of the classical theories from the social sciences. Stanford University: http://www.stanford.edu/ School of Engineering:
From playlist Engineering
Pierre Baudot : Information Topology: Statistical Physic of Complex Systems and Data Analysis
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 29, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
MIT 15.401 Finance Theory I, Fall 2008 View the complete course: http://ocw.mit.edu/15-401F08 Instructor: Andrew Lo License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 15.401 Finance Theory I, Fall 2008
How to simplify the difference quotient of a function
👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
From playlist Evaluate the Limit (PC)
Causality and Entanglement in Holography - The Connected Wedge Theorem Revisited - Jonathan Sorce
IAS It from Qubit Workshop Workshop on Spacetime and Quantum Information Tuesday December 6, 2022 Wolfensohn Hall One puzzling aspect of holography is that it conjectures a duality between a physical theory with a single rigid causal structure (the non-gravitational "boundary theory") and
From playlist IAS It from Qubit Workshop - Workshop on Spacetime and Quantum December 6-7, 2022