Question 1: A risk averse agent, whose utility is given by U(r) = In r and whose wealthis 50,000 is faced with a potential loss of 10,000 with a probability of 0.1. What is themaximum premium he would be willing to pay to protect himself against this loss? Whatis the minimum premium that an insurer, with the same utility function and wealth1,000,000 will be willing to charge to cover this loss? Explain the difference beteen thetwo figures.

Given: Utility function of risk averse agent is u(x)=ln(x) and wealth is 50,000 is faced with a…

Answered: Question 1: A risk averse agent, whose…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.4: Expected Value

Problem 1E: If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the...

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the expected value of this game is E=0.9+0.1= .
Question 3 Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will be equal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their income will be y − L. The chance of a safe return is 50%. Now suppose that there are two identical merchants, A and B, who are both risk averse expected utility maximisers with utility of income given by u(y) = ln y. The income of each merchant will be 8 if their own ship returns and 2 if it sinks. As previously, the probability of a safe return is 50% for each ship. However, with probability p ≤ 1/2 both ships will return safely. With the same probability p both will sink. Finally, with the remaining probability, only one ship will return safely. (iv) Compute the increase in the utility of each merchant that they could achieve from pooling their incomes (as a function of p). How does the benefit of pooling depend on the probability p? Explain intuitively why this…
Question 17 Suppose Carole has a total wealth of $100,000 and a utility described by U = E -A She has a risk aversion coefficient of A-1. She can borrow and lend/invest at the risk-free rate of 2.8%. Suppose the optimal risky portfolio has an expected return of 12% and a standard deviation of 27.5%, What is her optimal amount to borrow or lend/invest at the risk free rate? Indicate investing/lending as a positive number and borrowing as a negative number. Round to the nearest cent ($0.01). Your answer should not include the $ sign. If your answer is $25.34, it should be written as 25.34. Question 18 Ayear ago, an investor bought 200 shares of a "no-load" mutual fund at $10.01 per share. No-load funds do not change "entry fees or "exit" fees when buying or redeeming shares. Sometime during the year, the fund paid dividends of $0.71 per share and the fund paid capital gains of $0.14 per share - and these payments were reinvested in the fund at an average price of $10.73 per share…
J 2 10. Airlines routinely overbook flights to help lower the number of empty seats on their airplanes in order to increase profits. In the year 2005, the no-show rate was estimated to be 12%, with 88% of passengers with tickets actually showing up to take the flight. Suppose an airplane has 25 seats, and that the airline has sold 27 tickets. What is the probability that there will not be enough seats? 11. Referring to the no-show rates from Problem 10, out of 27 tickets sold, what are the mean and standard deviation for the number of people that show up to take the flight need answer for 11!
Question 2 Ignore the term "maximum likelihood"
Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million production facility. The decision tree is shown in Figure 4.16. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $59 million.…
QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesis
2.1 The demand for a product varies from month to month. Based on data from past years, the following probability density function shows the probabilities of MNM company’s monthly demand. Probabilities of MNM company's monthly demand Unit Demand P(X=x) 1200 0.19 2100 0.30 3300 0.40 3800 0.11 a) What is the probability that MNM will sell 3300 units next month? b) Given the information above, how many units can they expect to sell in a month?
Question 4 A country club wants to exam the effects of a new marketing campaign that attempts to get more people within the community to become members. In many communities, when people buy a house in the area, they receive a “Welcome Wagon” gift basket containing coupons to local restaurants. The idea of the marketing campaign is to include a free two month membership to the country club in the gift basket with the hope that once “new” residents try the country club then at least a certain proportion will want to become real members. One member of the Club’s Executive Council believes that at least 25% of the people who receive the coupons for the free membership will use the coupon. When testing the hypothesis that at least 25% of the people who receive the coupons for the free membership will use the coupon, what is the null and alternative hypothesis?
Question 6A A hamburger chain found that 75% of all customers use mustard, 80% use ketchup, and 65% use both, when ordering a hamburger. What is the probability that a customer chosen a random uses mustard given that the person is a ketchup-user? a.0.5200 b.0.9000 c.0.8125 d.0.8667 Question 6B A manufacturer of cutting and welding products makes an acetylene gas cylinder used in welding. The amount of nitrogen gas in the cylinder is normally distributed with mean 124 m3 and a standard deviation of 12 m3 … X~N(124, 122) P(X > 110) is ? a.0.1210 b.- 1.17 c.0.8790 d.0.3790
b) You decide to buy 10,000 shares of each company. If the covariance between ABC and XYZ is 0, what is the expected return and standard deviation of your portfolio over the next year? 1

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