For a disability insurance claim: (i) The claimant will receive payments at the rate of 20,000 per year, payable continuously as long as she remains disabled. (ii) The length of the payment period in years is a random variable with the gamma distribution with parameters a= 2 and 0 = 1. That is f(t) = te-t (iii) Payments begin immediately. (iv) 8 = 0.05 Calculate the actuarial present value of the disability payments at the time of disability. (A) 36,400 (E) 40,000 (B) 37,200 (C) 38,100 (D) 39,200
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- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?You are given:(i)Losses on an insurance coverage follow a lognormal distribution with parameters μ = θ and σ = 2.(ii) θ varies by policy holder in accordance with a normal distribution with mean 5 and variance 3.(iii) A policyholder submits 20 claims for losses. The average size of the claims is 10,000.Calculate the Buhlmann prediction of the size of the next loss for this policyholder.
- Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with µ = 0.1, o = 0.2, and time step At = 1/52 (weekly). Let St be the price of the stock at time t. If So = 100, and the first simulated (randomly selected) standard normal variable is e = -0.591, what is the simulated return over the next week? (a) -0.061 (b) -0.015 (c) 0.061 (d) -0.093Weekly rates of return (on an annualized basis) for certain securities over a given period are believed to be normally distributed with a mean of 8.00% and variance of 0.25. Give two values x, and x, such that you are 95% sure that annualized weekly returns will be between the two values.Structures in a county need to be designed for earthquake loading. After a detailed seismic risk analysis of the county, it is observed that the peak ground acceleration A observed in an earthquake event can be modeled by an exponential distribution with a mean of 0.2g. If A exceeds 0.4g, structures in the county will suffer significant damage. Assume that earthquakes occur on the average once every 2 years in the county, and the damage from different earthquakes is statistically independent. (a) What is the probability that there will be exactly two earthquakes in the next 50 years? (b) What is the probability of significant structural damage in an earthquake? (c) What is the probability of no significant structural damage due to earthquakes in a year? (d) What is the probability of no significant structural damage due to earthquakes in the next 50 years?
- Suppose that an item has a hazard rate function X(t) = 2.4t², t> 0. What is the probability that (a) the item survives to age 0.5? (b) the item's lifetime is between 1.5 and 3? (c) a (-year-old item will survive to age 3?If the expected return on the market is 8% and the risk for your rate is 4%. What is the expected return for a stock with a beta equal to 2.00? The time between customer arrivals at a furniture store has an approximate exponential distribution with mean θ = 8.5 minutes. If a customer just arrived, find the probability that the next customer will not arrive for at least 20 minutes.
- Rate of Return Month Apr-18 May-18 Jun-18 Jul-18 Aug-18 Sept-18 Oct-18 Nov-18 Dec-18 Jan-19 Feb-19 Rates of return of the index, x 4.23 3.25 - 1.78 - 3.20 1.29 3.58 1.48 - 4.40 -0.86 - 6.12 - 3.48 Rates of return of the company stock, y 3.28 5.09 0.54 2.88 2.69 7.41 - 4.83 -2.38 2.37 - 4.27 -3.77Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with A = 1, (which is identical to a standard gamma %3D distribution with a = 1), compute the following. (If necessary, round your answer to three decimal places.) (a) The expected time between two successive arrivals (b) The standard deviation of the time between successive arrivals (c) P(X < 4) (d) P(1 < X < 5)The Index of Industrial Production (IPt) is a monthly time series that measures the quantity of industrialcommodities produced in a given month. This problem uses data on this index for the United States. Allregressions are estimated over the sample period 1986:M1–2013:M12 (that is, January 1986 through December2013). Let Yt = 1200 × ln(IPt/IPt−1).(a) A forecaster states that Yt shows the monthly percentage change in IP, measured in percentage points perannum. Is this correct? Why?(b) Suppose she estimates the following AR(4) model for Yt:Yˆt = 0.787 + 0.052Yt−1 + 0.185Yt−2 + 0.234Yt−3 + 0.164Yt−4Use this AR(4) to forecast the value of Yt in January 2014, using the following values of IP for July 2013 throughDecember 2013:Table 1:Date 2013 M:7 2013 M:8 2013 M:9 2013 M:10 2013 M:11 2013 M:12IP 99.016 99.561 100.196 100.374 101.034 101.359(c) Worried about potential seasonal fluctuations in production, she adds Yt−12 to the autoregression. Theestimated coefficient on Yt−12 is 0.061, with…