2. Claim events on a portfolio of insurance policies follow a Poisson process with parameter A. Individual claim amounts follow a distribution X with density: f(x)=0.0122re001, g>0. The insurance company calculates premiums using a premium loading of 45%. (a) Derive the moment generating function Mx(t).
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- I'm working on inflation forecasting with quarterly inflation data for 1960 to 2022 using ARIMA model. The initial data is non-stationary. After the first differencing, based on the results of the p-value, it shows that the data is stationary. Then plot the ACF and PACF after first differencing, as attached pictures.With the graph of ACF and PACF, how can I define p, d, q for my ARIMA (p, d, q) model?ThankyouA standard "money demand" function used by macroeconomists has the form In(m) = Bo + B, In(GDP) + B2R, Where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of the nominal interest rate measured in percent per year. Supposed that B, = 2.15 and B, = -0.06. %3D What is the expected change in m if GDP increases by 3%? The value of m is expected to V by approximately%. (Round your response to the nearest integer) What is the expected change in m if the interest rate increases from 1% to 9%? The value of m is expected to ▼ by approximately %. (Round your response to the nearest integer)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 -3.77
- (d) At any time, find the mean age of insects in the population. (e) Sketch g(x), the p.d.f. of the age distribution of insects in the population. (f) No calculations are required for this part of the question.Now suppose that a population with the life table function Q(x) thatyou obtained in part (b) is stable but not stationary. Describe brieflyhow the age distribution of the population would differ from that of astationary population with the same life table function if the populationis (i) growing, (ii) declining. Draw rough sketches to show what thep.d.f. of the age distribution might look like in each case.Suppose that G is a function of a stock price, S and time. Suppose that σs and og are the volatilities of S and G. Show that when the expected return of S increases by Aos, the growth rate of G increases by AoG, where A is a constant.None
- Let X be a Poisson distribution with A as parameter: a. Find E(X) and VAR(X) b. Find the moment-generating functionFind the mean and standard deviation for each uniform continuous model U(1, 13) U(70, 200) U(3, 92)In bucolic farm there a contagion spreading among 500 happy cows, some with spots others with- out. There are no other breeds of cows in the field. The contagion spreads through contact. Cows without spots that come in to contact with cows with spots immediately develop spots. Assume that during the modeling period the effects are immediate and permanent (spotted cows remain spotted). It is reasonable to assume that the rate at which cows develop spots is proportional to the product of the number of spotted cows and the number of non-spotted cows. Let S = S(t) be the number of spotted cows at time t. Write a differential equation reflecting the situation.
- If F(x) is the cumulative distribution function (CDF) for X ~ Poisson (1.6), find the following values: a) F(0) b) F(1.2) c) F(2) c) F(-4.5)b) Explain how X can be related to the exponential distribution by using a moment generating function argument.(b) The distribution of claim size, X (in thousands of pounds), for a certain portfolio is modelled by the following probability density function f(x) = 1½ (ex/2 + xe x/2) x≥0. (i) Find the moment generating function for the claim size X. (ii) Obtain the mean, α2, variance and α3 for the claim size X. (iii) (iv) (v) The risk of claims for this portfolio is said to be homogenous with an average number of claims per year of 75. Find the mean, variance and skewness coefficient of the total annual claim size. The company applies a 6% safety loading for the policies in the portfolio. Estimate the initial reserve for the portfolio that would ensure that the total claims S for one year are covered with a probability of 99.95%, using skewness correction. If the company starts with an initial reserve of £125,000 find out the probability of meeting all claims in one year, using a skewness correction.
