Question: Q: The unit price of a certain commodity evolves randomly from day to day with a general downward drift but with an occasional upward jump

Q: The unit price of a certain commodity evolves randomly from day to day with a general downward drift but with an occasional upward jump when some unforeseen event excites the markets. Long term records suggest that, independently of the past, the daily price increases by a dollar with probability 0.45, declines by 2 dollars with probability 0.5, but jumps up to 10 dollars with probability 0.05. Let C0 denote the price today and Cn the price n days into the future. How does the probability P(Cn > C0) behave as n approaches infinity?

I started with markov chains but was concerned my result. Is this the correct method to implement to solve this question?

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