Question

Assume the unit price for a certain commodity follows this behavior: every day independently of every other day, there is a 50% chance the commodity price increases by $1, there is a 40% chance the commodity prices decreases by $3, and there is a 10% chance the commodity price increases by $5. Let C_0 be the price of the commodity today, and let C_n be the price of the commodity n days from now. What happens to P(C_n > C_0) as n→∞? (In words, what is the probability that the commodity price will be higher than today's price, in a very long time?)

Answer 1

Answer:

Given that,

Assume the unit price for a certain commodity follows this behavior:

Every day independently of every other day, there is a 50% chance the commodity price increases by $1, there is a 40% chance the commodity prices decreases by $3, and there is a 10% chance the commodity price increases by $5.

Let C_0 be the price of the commodity today, and let C_n be the price of the commodity n days from now.

What happens to P(C_n > C_0) as n→:

Expected change in price = Probability of price increasing by $1 $1 + Probability of price decreasing by $3 $3 + Probability of price increasing by $5 $5

Expected change in price = 0.5 1 + 0.4 (-3) + 0.1 5 = -0.2

Thus we can say that every year price fall by 20%

We can say that P(C_n) would be much lower than P(C_0).

As n tends to infinite, P(C_n) will tends towards zero or there is 0% probability that price would be more than today's price.