CQF-Computational finance problems & solutions at findtutoronline.net
1. Let be a random variable representing individual loss in the current year. We have
Next year's loss, , has same distribution as , i.e.,
This means is Pareto with parameters and (i.e., 700 and 3). Therefore,
Hence,
Therefore, for the random variable representing next year's individual losses limited to 2000 per loss, we h
ave
Loss amount with a 200 deductible per loss is the random variable defined as
Therefore,
and
It follows that
Further,
It follows that the standard deviation of is
2. The moment generating function of is
The cumulant generating function of is
For the th central moment of is
Thus, the th central moment of is times the th raw moment of .
3. The probability density functions of the three distributions are
Note that
Therefore, the loglogistic distribution has heavier tail than the lognormal distribution. Likewise,
When , this limit is zero, i.e., inverse gamma has the heaviest tail followed by loglogistic and then lognormal. On the other hand, if , , i.e, log-logistic has the heaviest tail. To compare inverse gamma with lognormal, we
observe that
Therefore, when loglogistic has the heaviest tail, followed by inverse gamma and then lognormal.
4. Here, can be written as
where are iid , are iid and is , and . We compute
Armed with these five probabilities, we are now ready to compute the requisite probabilities.
5. The inverse gamma probability density function is
Assuming , the mean and the variance are
By setting both equal to 1, we have , . We need to find
where is obtained from the equation
We observe, by substituting that
which is equal to 0.95 when , i.e., . It follows that
For more info, Pl do visit at www.findtutoronline.net & follow us at twitter & facebook. Give us a call at +91-8697669523
Ranadeb Singha MBA,CMA,BCOM(H),SAP Certification
Written by
Ranadeb Singha MBA,CMA,BCOM(H),SAP Certification
LikeCommentShare on LinkedInShare on FacebookShare on Twitter0 comments
Ranadeb Singha MBA,CMA,BCOM(H),SAP Certification Be the first to comment and start the conversation!
