Suppose that the classical risk model applies. Let (U(t)) to denote thesurplus process, that is,U(t) = u + ct – S(t),where the aggregate claims process (S(t))t≥o is a compound Poisson process withPoisson parameter λ =4. Assume that the premium income rate per time unit is= 16, where the time-unit is a day, and that u = 50. Assume that the individualclaims, denoted by X₁, i E N, are distributed according to a Gamma distributionX₂ ~ I(2, 4).Let (S(t)) to be the compound Poisson process from (c) and consideranother compound Poisson process (S(t))+zo whose jumps are given by a collec-tions of independent and identically distributed random variables {Y} which areindependent of {X₂}₁ but have the same distribution, that is, Y; ~ Gamma (2, 4).Moreover, assume that (S(t))+>o and (Ŝ(t))+>o jump at the same times; in otherwords, the underlying Poisson process that specifies the times of jumps is the samefor the two processes. Prove that for all t≥ 0, we haveE[S(t)S(t)] = 4t² + t.

Prove that for all ., given the following: are compound Poisson processes with jumps at the same…

Answered: Suppose that the classical risk model…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. Consider an individual with initial wealth W = $1,000 and utility function over money given by u(w) = w}. The individual faces loss of L = $800 with probabil- ity . Suppose an insurance is available at price $p per unit, where one unit of insurance pays the insured $1 if loss occurs and $0 otherwise. (a) What is the fair price for this insurance, and how much insurance will the individual buy at this price? (b) Suppose p = $0.3. How much insurance will the individual buy? (c) Suppose p = $0.3, but now the individual's utility function over money is u(w) = w². How much insurance will the individual buy? As clarified in the class, assume that the individual cannot insure more than the amount of loss.
10. Stock J has a beta of 1, an expected return of 15%. The equity risk premium is 10%, and the risk-free rate is 2.5%. Calculate Jensen's alpha measure for Stock J. (a) 2.5% (b) -2.5% (c) 0% (d) -7.5%
6. The demand function for the Viking Boat's 34-ft Sundancer yacht is p- 200-0.01zIn z, where z denotes the number of yachts and p is the price per yacht in hundreds of dollars. (a) Find the revenue function R(x) = rp and the marginal revenue function for this model of yacht. (b) Use the result of part (a) to estimate the revenue realized from the sale of the 501-st 34-ft Sundarce yacht. (Note: This is an estimate, so be careful to se the correct function from part (a) and to evaluate it at the correct value of r.) Note: If you compute the cract revenue lrom the sale of the 501st vacht, vou will find R(501)-R(500) = [200(501)-0.01(5501)'In(501)]-[200(500)-001(500) In(500)] 132.77676, so that the actual revenuoe is $13277.68 (c) Is the approKinalon gooxi?
Show that f (x) = 1 is Libschitz function on %3D x + 1 Upload
Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.
The team meeting will be held in 3 days from the date of the assignment and because of the limitation of time the Chief economist has given you the following guidelines: (a) Is there a trend in total accidents? (b) Is there seasonality in total accidents? (c) Consider the following change in the time series model: y; = P1yt-1 + ut where ut follows a white noise process. What is the condition we need to impose on p1 in order for the series yt to be weakly stationary? Why? (d) Consider the following change in the time series model: y; = Bo + B1x1-1+ B2xt-2 + u where y, is some outcome variable of interest, and x-1 and x-2 are strictly exogenous explanatory variables. How would you test for the presence of serial correlation in the residual uz? (e) Briefly explain how you would carry out econometric analysis of the model in (d) if u, is found to be stationary, but positively serially correlated.
10. You are given: i) The annual benefit premium for a fully continuous 20- year endowment insurance of 1000 on (55) is 15. ii) The annual benefit premium for a fully continuous 5 -year endowment insurance of 1000 on (70) is 121. iii) d=0.09 Calculate the 15th terminal benefit reserve on the 20- year endowment in- surance.
7. (a) If land that can be farmed L is eroding continuously at a rate of 4.5% per year because of changing climatic conditions, how much of this land will be left after 25 years? (b) A piece of art currently worth $2500 is appreciating in value 'V' according to the formula: 2500et0.5 However, assuming continuous discounting, the present value of V is given by: P = Vert = How long should the piece of art by kept to maximise its present value under continuous compounding with: (i) r = 0.05 (ii) r = 0.09
Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 1.4 14 % 23 % B 1.6 16 14 C 1.8 18 17 a. If σM = 22%, calculate the variance of returns of securities A, B, and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected return is given by E[R].
Please explain why this statement is true or false:"In the two-period model, both the Current Account and the Trade Balance in period one improve with an anticipated increase in the endowment of period two (ΔQ1=0 and ΔQ2>0)''Use equations of the optimal allocation of consumption in periods 1 and 2, the trade balance in period 1, and the current account in period 1 to support your answer.Assume the following lifetime utility function: U(C1,C2)= ln(C1) +β ln(C2) and the subjective discounting factor is 0<β<1
1. For a fully continuous whole life insurance of 1000 on (x), i) µx(t) = 0.04 ii) 8 = 0.02 iii) The contract premium is 120% of the benefit premium. Calculate E,L|T(r) > 5, the expected prospective loss at the end of the fifth year.

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