Consider the following payoff table. States of Nature B 150 100 0.6 Alternatives Alternative 1 A 100 Alternative 2 Probability 200 0.4 ow much should be paid for a perfect forecast of the state of nature?
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Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
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- Consider the following payoff matrix.As these researchers state, “Robbing a bank is the staple crime of thrillers, movies and newspapers. But . . . bank robbery is not all it is cracked up to be.” The researchers concentrated on the factors that determine the amount of proceeds from bank robberies, and thus were able to work out both the economics of attempting one and of preventing one. In particular, the researchers revealed that the return on an average bank robbery per person per raid is modest indeed—so modest that it is not worthwhile for the banks to spend too much money on such preventative measures as fast-rising screens at tellers’ windows. The researchers obtained exclusive data from the British Bankers’ Association. In one aspect of their study, they analyzed the data from a sample of 364 bank raids over a several-year period in the United Kingdom. The following table repeats a portion of Table 1 on page 19 of the article. ariable Mean standar deviation Amount stolen (pounds sterling) 20,330.50 53,510,2…As these researchers state, “Robbing a bank is the staple crime of thrillers, movies and newspapers. But . . . bank robbery is not all it is cracked up to be.” The researchers concentrated on the factors that determine the amount of proceeds from bank robberies, and thus were able to work out both the economics of attempting one and of preventing one. In particular, the researchers revealed that the return on an average bank robbery per person per raid is modest indeed—so modest that it is not worthwhile for the banks to spend too much money on such preventative measures as fast-rising screens at tellers’ windows. The researchers obtained exclusive data from the British Bankers’ Association. In one aspect of their study, they analyzed the data from a sample of 364 bank raids over a several-year period in the United Kingdom. The following table repeats a portion of Table 1 on page 19 of the article. ariable Mean standar deviation Amount stolen (pounds sterling) 20,330.50 53,510,2…
- Data on the 4000 largest mutual funds shows which funds provided a high 5-year return and a high 10-year return. Of the 4000 mutualfunds surveyed, 3000 funds had a high 5-year return, 2000 had a high 10-yearreturn, and 1500 had both a high 5-year return and a high 10-year return Given that a mutual fund had a high 5-year return, what is theprobability of a mutual fund having a high 10-year return?Explain with all necessary mathematical details as how would you determine the risk-neutral geometric Brownian motion price of an up-and-out European barrier option using the multiperiod binomial model?For the following payoff table determine the value of the and optimal mixed strategy for each player using graphical procedure. Player-2 Strategy 1 2 3 Player-1 1 2 0 3 2 3 1 2
- The government is attempting to determine whetherimmigrants should be tested for a contagious disease. Let’sassume that the decision will be made on a financial basis.Assume that each immigrant who is allowed into the countryand has the disease costs the United States $100,000, andeach immigrant who enters and does not have the diseasewill contribute $10,000 to the national economy. Assumethat 10% of all potential immigrants have the disease. Thegovernment may admit all immigrants, admit no immigrants,or test immigrants for the disease before determiningwhether they should be admitted. It costs $100 to test aperson for the disease; the test result is either positive ornegative. If the test result is positive, the person definitelyhas the disease. However, 20% of all people who do havethe disease test negative. A person who does not have thedisease always tests negative. The government’s goal is tomaximize (per potential immigrant) expected benefits minusexpected costs. Use a decision…The following payoff table provides profits based on various possible decision alternatives and various levels of demand. ALTERNATIVE DEMAND LOW MEDIUM HIGH Alternative 1 40 80 150 Alternative 2 80 120 130 Alternative 3 100 100 100 a. Which alternative would a pessimist choose? b. Which alternative would an optimist choose? c. Which alternative should be chosen using the Hurwicz decision criterion with α = 0.4?Given the following payoff table with the profits ($m), a firm might expect alternative investments (A, B, C) under different levels of interest rate (attached) (a) Which alternative should the firm choose under the maximax criterion? (b) Which option should the firm choose under the maximin criterion? (c) Which option should the firm choose under the LaPlace criterion? (d) Which option should the firm choose with the Hurwicz criterion with α = 0.2? (e) Using a minimax regret approach, what alternative should the firm choose? (f) Economists have assigned probabilities of 0.35, 0.3, and 0.35 to the possible interest levels 1, 2, and 3 respectively. Using expected monetary values, what option should be chosen and what is that optimal expected value? (g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret (h) Use the alternative method to verify EVPI
- Consider an economy with two states of nature and one time period. An option pays $3 in state 1 and $0 in state 2, and is being traded for the price of $1. A forward contract pays $3 in state 1 and -$2 in state 2. Using this information, compute the risk-free rate and the risk-neutral probabilities for each state of nature.There is some evidence that, in the years 1981-85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6, pp. 320-35,1987.) Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.87 %, with a standard deviation of 16 %. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years. (a) According to Chebyshev's theorem, at least…Use the following two tables to answer questions a. - e. a. Which of the above securities cannot lie on the efficient frontier? b. Why might you nonetheless include it in your portfolio? c. What is the expected return for a portfolio comprised of 40% security B and 60% security C? d. What is the standard deviation for a portfolio comprised of 40% security B and 60% security C? e. Suppose a risk-free asset with a yield of 3% exists, but only for lending. Would the highly risk-averse investor's optimal portfolio be likely to contain asset C? Why or why not?