Problem Solving Assignment: Mathematics Contingent Claims (Math Problem Sample)
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Mathematics of Contingent Claims
1] How many rolls of a k- side dice should you expect to make before all numbers 1,2…k have been seen at least once
Assuming that the die is 6-sided, then if we roll once, then we could roll and get 5 different sides when we roll
As such we get1/ (5/6) being 6/5 rolls, until the last success being 6/1
The probabilities of the geometric variables are then 6/6, 6/5,6/4,6/3,6/2 and 6/1
For the k-sided dice then the number of rolls is
1+k/ (k-1) + k/ (k-2) +â€¦+k/1=
Î£ k/1 =
k Î£ 1/i
The dice problem follows the Coupon Collectorâ€™s problem, where the success in each of the trails does not change, but then the probability of success reduces after each success (Tijms, 2012, pp 83-84). The Coupon Collector’s problem is also applicable using the Monte Carlo Simulation, where the number of rolls and sides per dice is considered.
2] Consider a dice game in which you are given at most n rolls to get the highest score possible. You final score is the number showing on the last dice rolled, when you either run out or you choose to stop. Find the optimal strategy for decid...
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