Reference no: EM13919198
Assignment- Optimal Stopping Rule for a Gambler (or City Trader)
Objective - To practice MATLAB and basic Simulation Techniques.
Problem - A gambler makes a series of plays with outcomes X1, X2,.... where the Xi, i ≥ 1 are independent, identically distributed random variables. The cost of each play is c. The gambler can stop at any time n ≥ 1 with the fortune:
Yn = max1≤i≤n Xi - cn
The gambler will stop if Xn > β. The gambler wants to maximize the mean of his fortune. What are the best values of β in the following two cases?
1. Case A: c = 0.2 and the distribution of Xn is the exponential distribution, i.e., its density function is
2. Case B: c = 0.1 and Xn is a discrete random variable obeying Poisson distribution:
P(x = k) = 1/ek! for k = 0, 1, 2,.....,
Task:
1. Find the best of values of β by using Monte Carlo simulation.
2. Write a report with the following sections:
- Problem: You should explain this problem in a way such that a 16-year old high school student can understand it.
- Method: You should describe and explain your method (not your matlab code) in details.
- Code: well-documented code.
- Experimental Results and Discussion: You report your experimental results here and give some discussions. You should use figures to show your results.
- Conclusion: Summarize what you have done and your reflection.
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Assignment- optimal stopping rule for a gambler
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