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17. Stochastic Processes II
 
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MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013 View the complete course: http://ocw.mit.edu/18-S096F13 Instructor: Choongbum Lee This lecture covers stochastic processes, including continuous-time stochastic processes and standard Brownian motion. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 102994 MIT OpenCourseWare
Business Math - Finance Math (7 of 30) Continuous Compounding
 
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Visit http://ilectureonline.com for more math and science lectures! In this video I will find the accumulated amount of a $2000 investment compounded continuously. Next video in this series can be seen at: http://youtu.be/jztNjV3vo4o
Views: 24269 Michel van Biezen
Compound interest introduction | Interest and debt | Finance & Capital Markets | Khan Academy
 
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Learn about the basics of compound interest, with examples of basic compound interest calculations. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/compound-interest-tutorial/v/the-rule-of-72-for-compound-interest?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Finance and Capital Markets channel: https://www.youtube.com/channel/UCQ1Rt02HirUvBK2D2-ZO_2g?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacadem
Views: 979055 Khan Academy
Infinite horizon continuous time optimization
 
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In this video, I show how to solve an infinite horizon constrained optimization problem in continuous time. I also show how the Hamiltonian approach works and why the first order condition are equal to what they are equal to. This allows viewers to solve more complicated problems as well.
Views: 5725 Constantin Bürgi
Using log continuous growth rates in finance
 
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Using log continuous growth rates with time-series financial data.
Views: 362 ProfGREvans
Option pricing in continuous time by Mrinal Ghosh (Part 1)
 
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Modern Finance and Macroeconomics: A Multidisciplinary Approach URL: http://www.icts.res.in/program/memf2015 DESCRIPTION: The financial meltdown of 2008 in the US stock markets and the subsequent protracted recession in the Western economies have accentuated the need to understand the dynamic interface between the modern financial sector and the overall macroeconomy. The dominant economic framework based on Neoclassical economics that informs policy making has turned out to be grossly inadequate for this purpose as it failed to either explain or predict the nature and cause of the sudden financial meltdown and the long economic recession that followed. The conceptual and methodological gaps and fault lines of the dominant framework have necessitated approaches that go beyond conventional analyses of individual or micro economic risk and the types failures caused by imperfect working of the price mechanism in financial markets. The challenge instead is to set the problem of modern finance in the macroeconomic context. This School aims to introduce the participants to the alternative analytical frameworks to study the workings of the modern financial sector and its implications to the economy as a whole. The modules in the School are organized in such a way that they progressively build on foundations starting from a critical perspective of macroeconomic analysis to lead the participants gradually to broader analysis beyond that is provided in the standard economic theory. The lectures will then build on this alternative conceptual perspective and explore and articulate alternative methodological frameworks in which the local or micro aspect of individual risk are integrated with the global or macro aspect of finance and money in the economy. The list of speakers includes renowned economists and mathematicians from India and abroad. ORGANIZERS: Vishwesha Guttal, Srikanth Iyer and Srinivas Raghavendra
Stopping time, hitting time and other times
 
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Stopping time, hitting time and other times.
Views: 11354 stepbil
Option pricing in continuous time by Mrinal Ghosh (Part 2)
 
01:45:51
Modern Finance and Macroeconomics: A Multidisciplinary Approach URL: http://www.icts.res.in/program/memf2015 DESCRIPTION: The financial meltdown of 2008 in the US stock markets and the subsequent protracted recession in the Western economies have accentuated the need to understand the dynamic interface between the modern financial sector and the overall macroeconomy. The dominant economic framework based on Neoclassical economics that informs policy making has turned out to be grossly inadequate for this purpose as it failed to either explain or predict the nature and cause of the sudden financial meltdown and the long economic recession that followed. The conceptual and methodological gaps and fault lines of the dominant framework have necessitated approaches that go beyond conventional analyses of individual or micro economic risk and the types failures caused by imperfect working of the price mechanism in financial markets. The challenge instead is to set the problem of modern finance in the macroeconomic context. This School aims to introduce the participants to the alternative analytical frameworks to study the workings of the modern financial sector and its implications to the economy as a whole. The modules in the School are organized in such a way that they progressively build on foundations starting from a critical perspective of macroeconomic analysis to lead the participants gradually to broader analysis beyond that is provided in the standard economic theory. The lectures will then build on this alternative conceptual perspective and explore and articulate alternative methodological frameworks in which the local or micro aspect of individual risk are integrated with the global or macro aspect of finance and money in the economy. The list of speakers includes renowned economists and mathematicians from India and abroad. ORGANIZERS: Vishwesha Guttal, Srikanth Iyer and Srinivas Raghavendra
5. Stochastic Processes I
 
01:17:41
MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013 View the complete course: http://ocw.mit.edu/18-S096F13 Instructor: Choongbum Lee *NOTE: Lecture 4 was not recorded. This lecture introduces stochastic processes, including random walks and Markov chains. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 261529 MIT OpenCourseWare
17. Options Markets
 
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Financial Markets (2011) (ECON 252) After introducing the core terms and main ideas of options in the beginning of the lecture, Professor Shiller emphasizes two purposes of options, a theoretical and a behavioral purpose. Subsequently, he provides a graphical representation for the value of a call and a put option, and, in this context, addresses the put-call parity for European options. Within the framework of the Binomial Asset Pricing model, he derives the value of a call-option from the no-arbitrage-principle, and, as a continuous-time analogue to this formula, he presents the Black-Scholes Option Pricing formula. He contrasts implied volatility, as represented by the VIX index of the Chicago Board Options Exchange, which uses a different formula in the spirit of Black-Scholes, with the actual S&P Composite volatility from 1986 until 2010. Professor Shiller concludes the lecture with some thoughts about options on single-family homes that he launched with his colleagues of the Chicago Mercantile Exchange in 2006. 00:00 - Chapter 1. Examples of Options Markets and Core Terms 07:11 - Chapter 2. Purposes of Option Contracts 17:11 - Chapter 3. Quoted Prices of Options and the Role of Derivatives Markets 24:54 - Chapter 4. Call and Put Options and the Put-Call Parity 34:56 - Chapter 5. Boundaries on the Price of a Call Option 39:07 - Chapter 6. Pricing Options with the Binomial Asset Pricing Model 51:02 - Chapter 7. The Black-Scholes Option Pricing Formula 55:49 - Chapter 8. Implied Volatility - The VIX Index in Comparison to Actual Market Volatility 01:09:33 - Chapter 9. The Potential for Options in the Housing Market Complete course materials are available at the Yale Online website: online.yale.edu This course was recorded in Spring 2011.
Views: 122153 YaleCourses
Financial Math for Actuaries, Lec 2: Valuation of Annuities (Level, Varying, Discrete, & Continuous)
 
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Playlist for problems on valuation of annuities: https://www.youtube.com/watch?v=nKtowv5gZwE&list=PLmU0FIlJY-MnsjhWSCBsXQit9lN8_x1cj
Views: 5875 Bill Kinney
Time value of money (using HP 10bII+)
 
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This is a quick tutorial on how to use HP 10bII+. The tutorial covers how to calculate: future value, present value, annuity, and net present value (NPV). You can find web-based practice problems at http://tinyurl.com/hp10biiplus. I recorded this faceless tutorial as a Teaching Assistant for ACC 312 (Fundamentals of Managerial Accounting) in Spring 2014.
Views: 140432 Daehyun Kim
Continuous Accounting - The Path to Building a Modern Finance Organization
 
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Finance and accounting leaders are expected to deliver accurate and real time analysis of their organization’s financial performance at all times. Yet many still wrestle with decades-old accounting processes that can only provide a view into the past, where the organization was, not where it is now. Continuous Accounting is a modern approach that empowers real time financial intelligence and allows finance and accounting teams to provide unprecedented value to the larger business.
Views: 4504 BlackLine
Time to Double Compounding Continuously
 
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Learn about the time to double when compounding continuously in this free math video tutorial by Mario's Math Tutoring. 0:12 Formula for Compounding Continuously 0:41 Example 1 Finding the Time to Double When Compounding Continuously 1:32 Using Natural Logs to Solve For t Related Videos: Time to Triple Compounding Continuously https://youtu.be/VFkHNsjyZys Compounding Continuously Pert Formula https://youtu.be/dFsBfi9W7sQ Looking to raise your math score on the ACT and new SAT? Check out my Huge ACT Math Video Course and my Huge SAT Math Video Course for sale at http://mariosmathtutoring.teachable.com For online 1-to-1 tutoring or more information about me see my website at: http://www.mariosmathtutoring.com * Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below) http://www.mariosmathtutoring.com/free-math-videos.html
Views: 6232 Mario's Math Tutoring
modelling of time in finance
 
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http://lapasserelle.com/finance in practice time is a continous variable. We show the formula for continuously compounded interests. However, for the sake of simplicity of explanations, in elementary finance time is treated as a discrete variable progressing in steps of one year.
Views: 129 andyfrc08
Paul Wilmott on Quantitative Finance, Chapter 3, First Stochastic Differential Equation
 
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In Chapter 3 I learned how to model asset prices using normal returns, both for discrete time and for continuous time using a Wiener process. The first stochastic differential equation!
Views: 51301 Nathan Whitehead
Exercise: Markowitz Portfolio Management in Continuous-Time (CRRA Preferences)
 
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Here is a small continuous-time finance exercise that shows that the optimal portfolio of a CRRA investor who can invest into log-normally distributed asset coincides with the Markowitz solution
HP10BII -- Introduction and 5-Key Time Value of Money Examples
 
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Free Online Textbook @ https://businessfinanceessentials.pressbooks.com/ This video introduces the HP10BII and walks through multiple examples of using the 5-key approach to solving basic Time Value of Money Examples. Includes changing periods per year, beginning vs. end of period payments, changing decimals displayed, solving for FV, PMT and rate of return.
Views: 221371 Kevin Bracker
Financial Derivatives - Lecture 11
 
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option valuation, option-pricing model, Black-Scholes Model, Black-Scholes-Merton Model, Robert Brown, Brownian Motion, random walk, stochastics, stochastic process, Bachelier, probability theory, stochasticv theory, Kiyoshi Ito, Ito Calculus, Stochastic Calculus, Continuous Time Finance, Robert Merton, Black-Scholes Value, tick, uptick., downtick, price jump, lognormal distribution, model assumptions, transaction costs,
Views: 1573 Krassimir Petrov
Arbitrage and Continuous Model in Advanced Financial Mathematics
 
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Educational video for all :) Credits to: My teammates -Aiman -Ihsan -Naja -Hamizah CS112 3C and everyone who made this video a success!
Views: 260 Mohamad Aiman
Brownian Motion (Wiener process)
 
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Financial Mathematics 3.0 - Brownian Motion (Wiener process) applied to Finance
Views: 100663 profbillbyrne
What is MATHEMATICAL FINANCE? What does MATHEMATICAL FINANCE mean? MATHEMATICAL FINANCE meaning
 
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What is MATHEMATICAL FINANCE? What does MATHEMATICAL FINANCE mean? MATHEMATICAL FINANCE meaning - MATHEMATICAL FINANCE definition - MATHEMATICAL FINANCE explanation. Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license. Mathematical finance, also known as quantitative finance, is a field of applied mathematics, concerned with financial markets. Generally, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain share price, a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock (see: Valuation of options; Financial modeling). The fundamental theorem of arbitrage-free pricing is one of the key theorems in mathematical finance, while the Black–Scholes equation and formula are amongst the key results. Mathematical finance also overlaps heavily with the fields of computational finance and financial engineering. The latter focuses on applications and modeling, often by help of stochastic asset models (see: Quantitative analyst), while the former focuses, in addition to analysis, on building tools of implementation for the models. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk- and portfolio management on the other. There exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing, and risk and portfolio management. One of the main differences is that they use different probabilities, namely the risk-neutral probability (or arbitrage-pricing probability), denoted by "Q", and the actual (or actuarial) probability, denoted by "P". Derivatives pricing: the Q world: The goal of derivatives pricing is to determine the fair price of a given security in terms of more liquid securities whose price is determined by the law of supply and demand. The meaning of "fair" depends, of course, on whether one considers buying or selling the security. Examples of securities being priced are plain vanilla and exotic options, convertible bonds, etc. Once a fair price has been determined, the sell-side trader can make a market on the security. Therefore, derivatives pricing is a complex "extrapolation" exercise to define the current market value of a security, which is then used by the sell-side community. Quantitative derivatives pricing was initiated by Louis Bachelier in The Theory of Speculation (published 1900), with the introduction of the most basic and most influential of processes, the Brownian motion, and its applications to the pricing of options. Bachelier modeled the time series of changes in the logarithm of stock prices as a random walk in which the short-term changes had a finite variance. This causes longer-term changes to follow a Gaussian distribution. The theory remained dormant until Fischer Black and Myron Scholes, along with fundamental contributions by Robert C. Merton, applied the second most influential process, the geometric Brownian motion, to option pricing. For this M. Scholes and R. Merton were awarded the 1997 Nobel Memorial Prize in Economic Sciences. Black was ineligible for the prize because of his death in 1995. A process satisfying (1) is called a "martingale". A martingale does not reward risk. Thus the probability of the normalized security price process is called "risk-neutral" and is typically denoted by the blackboard font letter " Q {\displaystyle \mathbb {Q} } \mathbb {Q} ". The relationship (1) must hold for all times t: therefore the processes used for derivatives pricing are naturally set in continuous time. The quants who operate in the Q world of derivatives pricing are specialists with deep knowledge of the specific products they model. Securities are priced individually, and thus the problems in the Q world are low-dimensional in nature. Calibration is one of the main challenges of the Q world: once a continuous-time parametric process has been calibrated to a set of traded securities through a relationship such as (1), a similar relationship is used to define the price of new derivatives. The main quantitative tools necessary to handle continuous-time Q-processes are Ito’s stochastic calculus and partial differential equations (PDE’s).
Views: 1493 The Audiopedia
Future Value Using Microsoft Excel-Continuous Compounding
 
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Homework assignment tutorial from Pyzdek Institute Six Sigma Black Belt Training.
Views: 18454 ThomasPyzdek
Continuous Accounting
 
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Continuous Accounting embeds automation, control, and period-end tasks within day-to-day activities, allowing the rigid accounting calendar to more closely mirror the broader business. Continuous Accounting transforms the way business process works by emphasizing real-time processing, especially skilled employees, and deep analysis. The result is a more efficient close, more accurate financials, and a more effective organization.
Views: 1338 BlackLine
Top 3 Books for Financial Success | Brian Tracy
 
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One of the best habits that you can develop is the habit of continuous learning. The most successful people including Bill Gates and Warren Buffett all praise the importance of reading. Today, I give you my 3 favorite books for personal and financial success. http://bit.ly/2EqflqR Also, if you'd like to enter my free giveaway, click the link above! “We live in the richest society in all of human history; are you getting your fair share?” @BrianTracy (Click to Tweet: https://ctt.ec/5cwfQ) ___________________ Learn more: Subscribe to my channel for free offers, tips and more! YouTube: http://ow.ly/ScHSb Facebook: http://www.facebook.com/BrianTracyPage Twitter: http://www.twitter.com/BrianTracy Google+: +BrianTracyOfficialPage Pinterest: http://www.pinterest.com/BrianTracy Instagram: @TheBrianTracy Blog: http://bit.ly/1rc4hlg
Views: 275311 Brian Tracy
Understanding Wavelets, Part 1: What Are Wavelets
 
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This introductory video covers what wavelets are and how you can use them to explore your data in MATLAB®. •Try Wavelet Toolbox: https://goo.gl/m0ms9d •Ready to Buy: https://goo.gl/sMfoDr The video focuses on two important wavelet transform concepts: scaling and shifting. The concepts can be applied to 2D data such as images. Video Transcript: Hello, everyone. In this introductory session, I will cover some basic wavelet concepts. I will be primarily using a 1-D example, but the same concepts can be applied to images, as well. First, let's review what a wavelet is. Real world data or signals frequently exhibit slowly changing trends or oscillations punctuated with transients. On the other hand, images have smooth regions interrupted by edges or abrupt changes in contrast. These abrupt changes are often the most interesting parts of the data, both perceptually and in terms of the information they provide. The Fourier transform is a powerful tool for data analysis. However, it does not represent abrupt changes efficiently. The reason for this is that the Fourier transform represents data as sum of sine waves, which are not localized in time or space. These sine waves oscillate forever. Therefore, to accurately analyze signals and images that have abrupt changes, we need to use a new class of functions that are well localized in time and frequency: This brings us to the topic of Wavelets. A wavelet is a rapidly decaying, wave-like oscillation that has zero mean. Unlike sinusoids, which extend to infinity, a wavelet exists for a finite duration. Wavelets come in different sizes and shapes. Here are some of the well-known ones. The availability of a wide range of wavelets is a key strength of wavelet analysis. To choose the right wavelet, you'll need to consider the application you'll use it for. We will discuss this in more detail in a subsequent session. For now, let's focus on two important wavelet transform concepts: scaling and shifting. Let' start with scaling. Say you have a signal PSI(t). Scaling refers to the process of stretching or shrinking the signal in time, which can be expressed using this equation [on screen]. S is the scaling factor, which is a positive value and corresponds to how much a signal is scaled in time. The scale factor is inversely proportional to frequency. For example, scaling a sine wave by 2 results in reducing its original frequency by half or by an octave. For a wavelet, there is a reciprocal relationship between scale and frequency with a constant of proportionality. This constant of proportionality is called the "center frequency" of the wavelet. This is because, unlike the sinewave, the wavelet has a band pass characteristic in the frequency domain. Mathematically, the equivalent frequency is defined using this equation [on screen], where Cf is center frequency of the wavelet, s is the wavelet scale, and delta t is the sampling interval. Therefore when you scale a wavelet by a factor of 2, it results in reducing the equivalent frequency by an octave. For instance, here is how a sym4 wavelet with center frequency 0.71 Hz corresponds to a sine wave of same frequency. A larger scale factor results in a stretched wavelet, which corresponds to a lower frequency. A smaller scale factor results in a shrunken wavelet, which corresponds to a high frequency. A stretched wavelet helps in capturing the slowly varying changes in a signal while a compressed wavelet helps in capturing abrupt changes. You can construct different scales that inversely correspond the equivalent frequencies, as mentioned earlier. Next, we'll discuss shifting. Shifting a wavelet simply means delaying or advancing the onset of the wavelet along the length of the signal. A shifted wavelet represented using this notation [on screen] means that the wavelet is shifted and centered at k. We need to shift the wavelet to align with the feature we are looking for in a signal.The two major transforms in wavelet analysis are Continuous and Discrete Wavelet Transforms. These transforms differ based on how the wavelets are scaled and shifted. More on this in the next session. But for now, you've got the basic concepts behind wavelets.
Views: 183140 MATLAB
Attract Abundance of Money Prosperity Luck & Wealth★Jupiter's Spin Frequency★Theta Binaural Beats
 
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Attract Abundance of Money Prosperity Luck & Wealth★Jupiter's Spin Frequency★Theta Binaural Beats by Binaural Beats Meditation (Good Vibes) Listen in a low volume but clearly audible. Having a mindset of gratitude will make you happier, healthier, more satisfied, you'll attract abundance and magnetize better experiences. Listen before sleep for 4 weeks-90 days. Headphones required. Affirmations: I feel Rich I love money. Money loves me. I attract money now I am very happy & grateful that money comes to me in increasing quantities from many sources on a continuous basis I am receiving money now I have more than enough money I am willing, ready and able to receive money I see abundance everywhere I am a money magnet I am grateful for what I already have and for all that I receive now. I have more than what I need Money now comes to me from unexpected sources & I am grateful My income is growing higher and higher I am a rich child of a loving universe I have the power to attract money I receive money happily now Money flows to me easily I am sensible with money and manage it wisely. I allow my income to constantly expand and I always live in comfort and joy. © Good Vibes all rights reserved.
Compound Frequencies (continuous vs. discrete)
 
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Two ways to look at this: start with a given rate (10% in this example) and use different compound frequencies, which gives different final (terminal values). Or, assume the same terminal value, and translate into different discrete interest rates (e.g., monthly, daily). But, the discrete rates can be translated to continuous and vice-versa.
Views: 7700 Bionic Turtle

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