An insurance company uses the model of collective risks in multiple periods by means of a Poisson-compound-Exponential process. The Poisson intensity equals 20, and the mean claim per period is of $140. The company plans to continuosly charge the equivalence premium with a loading percentage of 55%. What should the initial wealth of the company be, so that the probability of ruin is less than 5%?
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- I am in possession of two coins. One is fair so that it lands heads (H) and tails (T)with equal probability while the other coin is weighted so that it always lands H. Bothcoins are magical: if either is flipped and lands H then a $1 bill appears in your wallet,but when it lands T nothing happens. You may only flip a coin once per period. Theinterest rate is i per period. You are risk-neutral and thus only concern yourself withexpected values (and not variance). For simplicity, in the questions below assumeyou will live forever.1. How much are you willing to pay for such a coin that you know is fair? 2. How much are you willing to pay for such a coin that you know is weighted? 3. I currently own the coins and know which is fair and which is weighted, but youcannot tell which is which. You may make an offer to purchase a coin of yourchoosing, which I am free to accept or reject. What is the most you are willingto offer? Explain how you arrived at this answer.Probability Possible Rate of Return 0.25 -0.10 0.15 0.00 0.35 0.10 0.25 0.25 a. Under what conditions can the standard deviation be used to measure the relative risk of two investments? b. Under what conditions must the coefficient of variation (CoVar) be used to measure the relative risk of two investments?Question 2An investor is to purchase one of three types of real estate, as illustrated inFigure below. The investor must decide among an apartment building, anoffice building, and a warehouse. The future states of nature that willdetermine how much profit the investor will make are good economicconditions and poor economic conditions. The profits that will result fromeach decision in the event of each state of nature are shown in Table below: Assume that it is now possible to estimate a probability of 0.60 that goodeconomic conditions will exist and a probability of .40 that poor economicconditions will exist. a) Determine the best decision by using expected opportunity loss. b) Develop a decision tree, with expected values at the probability nodes. c) Compute the expected value of perfect information.
- Given that Z is distributed as a standard normal random variable, what is Pr(Z > -0.04)? Round your answer to three decimal places, e.g. 0.251.The weekly salary paid to employees of a small company that supplies part-time laborers averages s800 with a standard deviation of $500. (a) If the weekly salaries are normally distributed, estimate the fraction of employees that make more than $300 per week. (b) If every employee receives a year-end bonus that adds $100 to the paycheck in the final week, how does this change the normal model for that week? (c) If every employee receives a 5% salary increase for the next year, how does the normal model change? (d) If the lowest salary is $300 and the meltian salary is $550, does a normal model appear appropriate?The owner of a ski resort is considering installing a new ski lift that will cost $900,000. Expenses for operating andmaintaining the lift are estimated to be $1,500 per day when operating. The U.S. Weather Service estimates thatthere is a 60% probability of 80 days of skiing weather per year, a 30% probability of 100 days per year, and a 10% probability of 120 days per year. The operators of the resort estimate that during the first 80 days of adequate snow in a season, an average of 500 people will use the lift each day, at a fee of $10 each. If 20 additional days are available, the lift will be used by only 400 people per day during the extra period; and if 20 more days of skiing are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within five years and want at least a 25% per year rate of return before taxes. Based on a before-tax analysis, should the lift be installed?
- For all parts of this question, assume that the log of GDP per capita is normally distributed with a mean of 8.7 and standard devistion of 1.5Step 1 of 4: If the log of the world distribution of income is normaly distributed with a mean of 8.7 and a standard deviation of 1.5, what income indollars) marks the 90th percentile? KeypadAnswer A 71.325B 1.29C 41,253D 10.63a. If the decision maker knows nothing about the probabilities of the fourstates of nature, what is the recommended decision using:i. the optimistic approachii. the conservative approachiii. the minimax regret approachiv. the Laplace method53. The annual demand for Prizdol, a prescription drugmanufactured and marketed by the NuFeel Company,is normally distributed with mean 50,000 and standarddeviation 12,000. Assume that demand during each ofthe next 10 years is an independent random numberfrom this distribution. NuFeel needs to determine howlarge a Prizdol plant to build to maximize its expectedprofit over the next 10 years. If the company builds aplant that can produce x units of Prizdol per year, it willcost $16 for each of these x units. NuFeel will produceonly the amount demanded each year, and each unit ofPrizdol produced will sell for $3.70. Each unit of Prizdol produced incurs a variable production cost of $0.20.It costs $0.40 per year to operate a unit of capacity.a. Among the capacity levels of 30,000, 35,000,40,000, 45,000, 50,000, 55,000, and 60,000 unitsper year, which level maximizes expected profit?Use simulation to answer this question.b. Using the capacity from your answer to part a,NuFeel can be 95%…
- The Kwik Klean car wash loses $250 on rainy days and gains $1200 on non rainy days. If the probability of rain is 0.13, what is the expected net profit?Question10: He game matrix table arranged in terms of player A is given. by solving the game with the graphic method; 2-)Find the probability of playing B's 1st strategy. 2-)Find the probability of playing B's 2nd strategy. 3-) find the expected game value.The data from 200 machined parts are summarizedas follows:y yesdepth of boreE, noabovebelowedge conditioncoarsetarget15target10moderatesmooth25205080(a) What is the probability that a part selected has a moderateedge condition and a below-target bore depth?(b) What is the probability that a part selected has a moderateedge condition or a below-target bore depth?(c) What is the probability that a part selected does not have amoderate edge condition or does not have a below-targetbore depth?(d) Construct a Venn diagram representation of the events inthis sample space.
