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terminology - Is it more accurate to use the term Geometric …
WEBI'm probably wrong, but I think if people differentiate between the two: "geometric" implies rapid growth/decay but with a constant rate while "exponential" implies rapid growth/decay with an accelerating rate. I believe a lot of non-mathy people use "exponential" because it sounds impressive, more impressive than "geometric".
Math.stackexchange.comExpected Geometric Growth Rate (Kelly's Criterion)
WEBWhat is a good intuition for this notion of expected geometric growth rate to use as a stepping stone toward understanding Kelly Criterion? I am much more experienced in calculus than statistics, so if it results from a differential equation or recurrence relation that is easier to internalize than the solution itself, this may be helpful to know.
Math.stackexchange.comWhat are differences between Geometric, Logarithmic and …
WEBAug 3, 2020 · Logarithmic growth and exponential growth is inverse of one another. Difference between exponential growth and geometric growth is that as wikipedia has stated "In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression."
Math.stackexchange.comGeometric growth rate and Kelly's Criterion question
WEBFeb 17, 2022 · Derivation of the Kelly Criterion. The Kelly Criterion is derived by maximizing the expected geometric growth rate. E[1 nlogWn W0], which is not the same as. 1 nlogE(Wn) W0. The terminal wealth after n rounds is. Wn = W0 n ∏ k = 1(1 + fXk) Taking the logarithm of both sides we get. logWn = logW0 + n ∑ k = 1log(1 + fXk)
Math.stackexchange.comRate of growth of a geometric sequence - Mathematics Stack …
WEBAug 24, 2014 · The geometric sequence in your question is given by an+1 = (1 + r)an a n + 1 = (1 + r) a n with a0 = a a 0 = a. In every single "time step" going from n n to n + 1 n + 1 your an a n becomes (1 + r)an (1 + r) a n. So your growth rate per time step is r r. You cannot break up this time step into smaller units of time since n n in the geometric
Math.stackexchange.comExpectation of the maximum of i.i.d. geometric random variables
WEBThere is no nice, closed-form expression for the expected maximum of IID geometric random variables. However, the expected maximum of the corresponding IID exponential random variables turns out to be a very good approximation.
Math.stackexchange.comWhy does average annual growth overestimate true growth rate?
WEBJul 27, 2019 · If a company's shipments grew 100% from 100 to 200 and then in the next period fell 50% back 100, then the average annual growth rate would be 25%. But this growth rate is incorrect as you're back at your principal. A compounded annual growth rate calculation would yield the correct 0% annual growth rate. Why does AAGR …
Math.stackexchange.comHow to derive Gordon growth model - Mathematics Stack Exchange
WEBThe formula for the Gordon growth model is: $\hspace{1in}P= \sum_{t=1}^{\infty} D\times\frac{(1+g)^t}{(1+k)^t}$ So summing the infinite series we get: $\hspace{1in}P=\frac{D(1+g)}{k-g} \hspace{2in}\mbox{(1)}$ Here's my attempt to arrive at equation (1): The sum of a geometric series is: $\hspace{1in}\frac{a}{1-r}$ So, plugging in …
Math.stackexchange.comGeometric mean with negative numbers - Mathematics Stack …
WEBApr 3, 2022 · $\begingroup$ The geometric mean is a useful concept when dealing with positive data. But for negative data, it stops being useful. Even in the cases where it is defined (in the real numbers), it is no longer guaranteed to give a useful response. Consider the "geometric mean" of $-1$ and $-4$.
Math.stackexchange.comprobability - Maximizing Geometric Growth Rate (Kelly Formula) …
WEBSep 15, 2023 · Plug the fractional bet sizes back into the geometric growth rate formula and find the bet combination with the greatest R. Wager on the bet combination with the greatest R (from step 2) and bet bankroll fraction on each bet as calculated in step 1.
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