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If the price of every asset in a discrete model is strictly increasing, with probability one, then does the market admit arbitrage?

Thoughts: I believe this is true but I am not sure how to give an arbitrage argument to show that there exists some arbitrage strategy. Perhaps I am not understanding the implications of the question.

Any suggestions are greatly appreciated.

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Off the top of my head, if interest rates are zero or negative, then yes. Just borrow the purchase price and buy any asset. Sell later and pay off the loan. Otherwise no.

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  • $\begingroup$ I agree. If you can borrow at less than the returns from the assets specified above, it would be arbitrage. However, if you borrow at 10% and there's a range of returns on the assets between 5% and 15%, this is not arbitrage. $\endgroup$ – RandyF Dec 2 '16 at 18:10

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