Question: 1. Consider S = X1 + X2 + ... + Xn, where X; ~ Fx(2) provided below, N Poisson() and the random variables respect all

1. Consider S = X1 + X2 + ... + Xn, where X; ~

1. Consider S = X1 + X2 + ... + Xn, where X; ~ Fx(2) provided below, N Poisson() and the random variables respect all the compound model's assumptions. 2 M Fx(x) = lo aj 213-1e-2/0 "0"3 (r; 1)dz j=1 (a) Derive the moment generating function of S (b) Find E(X), E(S) and Var(S) (c) Provide a function in R which returns the quantiles of S (d) Provide a code for M = 2, fix a; (0.7,0.3), r; (1,2), 0 = 0.5 and = 1.2 which calculates VaR (S) and find VaR0.95(S). (e) For M = 2, fix a; = (0.7,0.3), r; = (1, 2) and 6 = 0.5, find the theoretical VaR0.95(X) and compare with the answer your R code provides. = = 1. Consider S = X1 + X2 + ... + Xn, where X; ~ Fx(2) provided below, N Poisson() and the random variables respect all the compound model's assumptions. 2 M Fx(x) = lo aj 213-1e-2/0 "0"3 (r; 1)dz j=1 (a) Derive the moment generating function of S (b) Find E(X), E(S) and Var(S) (c) Provide a function in R which returns the quantiles of S (d) Provide a code for M = 2, fix a; (0.7,0.3), r; (1,2), 0 = 0.5 and = 1.2 which calculates VaR (S) and find VaR0.95(S). (e) For M = 2, fix a; = (0.7,0.3), r; = (1, 2) and 6 = 0.5, find the theoretical VaR0.95(X) and compare with the answer your R code provides. = =

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