# Is there an arbitrage strategy if short selling of a stock is allowed?

Consider a market with a risk-free asset such that $$A(0) = 100, A(1) = 110, A(2) = 121$$ dollars and a risky asset, the price of which can follow three possible scenarios

Is there an arbitrage strategy if short selling of a stock is allowed, but transaction costs of 5% of the transaction volume apply whenever stock is traded?

How can I solve this?

I know the the No-Arbitrage Principle would be violated if there was a self-financing predictable strategy with initial value $$V(0) = 0$$ and final value $$0 \neq V(2) \geq 0$$ such that $$V(1)<0$$ with positive probability

• thank you. when i attempted this, I got: The risk free rate is 10%. The guaranteed return on the stock from periods 1 to 2 in scenario 3 would be $\frac{1}{95} = 1.05%$ The net difference would be 8.95%. A transaction cost of 5% would make the difference 3.95%. The difference is still positive, so an arbitrage opportunity is still possible. – user477465 Nov 5 '18 at 19:33