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Has PDF. Publication Type. More Filters. With the aid … Expand. View 1 excerpt, cites background. Robust Growth-Optimal Portfolios. Highly Influenced. View 6 excerpts, cites background and methods. In this work we ask how should an investor distribute wealth over various assets to maximize the growth rate of the cumulative wealth in a discrete time market with proportional transaction costs. We … Expand. Ergodic robust maximization of asymptotic growth. The Annals of Applied Probability.

We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. View 7 excerpts, cites background. We consider asset allocation strategies for the case where an investor can allocate his wealth dynamically between a risky stock, whose price evolves according to a geometric Brownian motion, and a … Expand. We consider asset allocation strategies for the case where an investor can allocate his wealth dynamically between a risky stock , whose price evolves according to a geometric Brownian motion , and a … Expand.

Investing in a portfolio strategy, which maximizes the the expected logarithm of capital implies outperforming any other significantly different strategy, given knowledge of the true underlying … Expand. Mean-variance versus expected utility in dynamic investment analysis. View 2 excerpts, cites background. In this paper we introduce an empirical approximation of the log-optimal investment strategy that guarantees an almost optimal growth rate of investments.

The proposed strategy also considers the … Expand. View 3 excerpts, cites background. Publisher Summary Entrepreneurs have a given initial fortune and faces the following situation: during any time period, they may invest various amounts of their available fortune in various … Expand. View 1 excerpt. The "fallacy" of maximizing the geometric mean in long sequences of investing or gambling. Publisher Summary The chapter presents an alternative way to relate the expected utility and mean-variance approaches.

It presents proofs of the two general theorems involved in an aspect of the … Expand. View 1 excerpt, references background. Competitive Optimality of Logarithmic Investment. Optimal strategies for repeated games. The highest rating ever recorded for an earthquake is 9. An earthquake is measured with a wave amplitude times as great as A 0. What is the magnitude of this earthquake using the Richter scale, to the nearest tenth?

Use the Richter scale equation. Substitute this expression in for A. Use a calculator to evaluate the logarithm. The magnitude of this earthquake is 2. A difference of 1 point on the Richter scale equates to a fold difference in the amplitude of the earthquake which is related to the wave strength. This means that an earthquake that measures 3. In that example, the wave amplitude of the earthquake was times normal. What if it were 10 times that, or 3, times normal?

To find the measurement of that size earthquake on the Richter scale, you find log A calculator gives a value of 3. One extra point on the Richter scale can mean a lot more shaking! Sound is measured in a logarithmic scale using a unit called a decibel. The formula looks similar to the Richter scale:.

One hot water pump has a noise rating of 50 decibels. One dishwasher, however, has a noise rating of 62 decibels. The dishwasher noise is how many times more intense than the hot water pump noise? Start by finding the intensity of noise for the hot water pump. Divide the equations by 10 to get the log by itself.

Rewrite the equation as an exponential equation. Multiply by P 0 to get h by itself. Repeat the same process to find the intensity of the noise for the dishwasher. To compare d to h , you can divide. Use the laws of exponents to simplify the quotient. With decibels, every increase of 10 means the sound is 10 times more intense.

An increase of 20 would be 10 times more intense for the first 10, and another 10 times more intense for the second 10—so a sound that is 75 decibels is times more intense than a sound that is 55 decibels! The measure of acidity of a liquid is called the pH of the liquid. The formula for pH is:. Liquids with a low pH down to 0 are more acidic than those with a high pH. Water, which is neutral neither acidic nor alkaline, the opposite of acidic has a pH of 7.

If lime juice has a pH of 1. The concentration of hydrogen ions in lime juice is 0. An earthquake monitoring station measured the amplitude of the waves during a recent tremor. It measured the waves as being , times as large as A 0 , the smallest detectable wave. How high did this earthquake measure on the Richter scale? An earthquake that measured 1 on the Richter scale would have a wave amplitude of only 10 times greater than normal. To solve this problem, setup the equation as , and solve for R.

The correct answer is 5. An earthquake that measured 3 on the Richter scale would have a wave amplitude of 10 3 , or 1, times greater than normal. To solve this problem, set up the equation as , and solve for R. To find the Richter measure of an earthquake with waves , times greater than normal, solve. The answer is 5. An earthquake that measured 9 on the Richter scale would have a wave amplitude of 1,,, times greater than normal. Using Exponential Functions. Exponential functions are used for even more contexts, including population and bacterial growth, radioactive decay, compound interest, cooling of objects, and growth of phenomena such as virus infections, Internet usage, and popularity of fads.

For example, recall that the formula for compound interest is , where P is principal, A is amount, r is the annual rate, m is the number of compounding periods, and t is the number of years. Find values for the variables that you can. Divide both sides by P to get the exponential expression by itself. To solve an equation with the variable in the exponent, take logarithms of both sides. You can use any base, so log base 10 or ln base e would be best, then you can use a calculator to evaluate the logarithms.

Use the power property of logarithms to get the variable out of the exponent. Divide to get t by itself. Use the calculator to evaluate the logarithms. The money will double in about 7 years. Round to the nearest whole year. According to the U.

Census Bureau, the world population in was about 6. That is, it would increase about 1. If the world population grows by 1. The 1 represents the current population, and the.

Empirical Bayes stock market portfolios. View 7 excerpts, cites methods and background. Log-optimal currency portfolios and control Lyapunov exponents. Algoet and T. Cover characterized log-optimal portfolios in a stationary market without friction. There is no analogous result for markets with friction, of which a currency market is a typical … Expand. View 4 excerpts, cites methods and background.

Competitive Optimality of Logarithmic Investment. PpTO date, the bulk of portfolio theory has evolved on the basis of a single-period model. Those writers who have considered sequential portfolio models, for example Tobin [24] and Mossin [19], have … Expand. Multiasset portfolio selection models stated in terms of the expected utility criterion generally require the evaluation of multiple integrals. This reality has severely hindered attempts towards the … Expand. In [2] Hakansson and Liu presented a multiperiod portfolio model in which there is an optimal myopic policy.

In particular, at any decision point j and state m the optimal amount to invest in … Expand. Three main approaches to the problem of portfolio selection may be discerned in the literature. The first of these is the mean-variance approach, pioneered by Markowitz [21], [22], and Tobin [30]. On the robustness of the Arrow-Pratt risk aversion measure. A new interpretation of information rate. IRE Trans. Computation of channel capacity and rate-distortion functions.

IEEE Trans. Portfolio Choice and the Kelly Criterion. Related Papers. Abstract Citations 23 References Related Papers. By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy , Terms of Service , and Dataset License.

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Follow Download. Overview Functions Reviews 0 Discussions 1. Cite As Mo Chen Tags Add Tags gaussian pdf probability. Start Hunting! Discover Live Editor Create scripts with code, output, and formatted text in a single executable document. Select a Web Site Choose a web site to get translated content where available and see local events and offers.

Perhaps the most well-known application of exponential functions comes from the financial world. Suppose you have $ to invest at your local bank and they. It this case we solve for time where the future value of the investment is. 2P0 where P0 is the amount of our initial investment. Here are some sample problems. Draw the graph of each of the following logarithmic functions, and analyze each 15 $ is invested in an account that yeilds 5% interest per year.