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Problem 197 of 333MediumFinanceP197
The +50%/−40% coin game
You start with $100. Each round a fair coin is flipped: heads multiplies your money by 1.5, tails by 0.6.
(a) After 100 flips, what is your expected wealth, and what is your median wealth?
(b) What is the probability you finish ahead after 100 flips?
(c) Now you may put only a fraction of your wealth into each flip and keep the rest in cash. Which maximizes the long-run growth rate, and what is that rate?
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