代写ACTSC 625、代写Python，Java程序

日期：2022-04-12 11:18

ACTSC 625: Casualty and Health Insurance Mathematics

Winter 2022, Assignment 2

Consider the collective aggregate risk model

i=1 is a sequence of iid copies of X, which are all independent of N. The primary distribution

N  BIN(m; q) with m = 15 and q = 0:3 The secondary distribution X  EXP() with  = 15.

(1). Find an exact formula for the cdf of S.

(2). Discretize X with span h > 0, and denote the discretized random variable as Xb.

be the corresponding discretized aggregate risk. Use Panjerís recursion to compute the cdf FSb(x) at

x = nh for n = 0; 1; : : : ;

300

h. For h = 10; h = 5, h = 1, and h = 0:1, draw the absolute di§erence function

for x 2 f0; h; 2h; : : : ; 300g, respectively.

(3). For the discretized aggregate risk Sb, use the pmf method to compute the cdf FSb(x) at x = nh

for n = 0; 1; : : : ;

300

h

. Again, for h = 10; h = 5, h = 1, and h = 0:1, draw the absolute di§erence function

for x 2 f0; h; 2h; : : : ; 300g, respectively. Note: the pmf method involves the calculation of

inÖnite sum, which can be approximated by Önite sum, that is, you can impose some stopping rules.

(4). Draw some conclusion about the di§erences between these two approaches (Panjerís recursion and

pmf method) in terms of precision and computation time.

1