# Cost of a trading startegy [closed]

I have a question about the cost process of a trading strategy. Suppose we work in the finite discrete case and holding just one risky asset for simplicity. Let $\phi=(\theta,\eta)$, where $\theta$ should be predictable and models the amount of shares and $\eta$ models the bank account. Then the cost occuring over $k$ to $k+1$ are (working with discounted objects.)

$$\Delta C_{k+1}=C_{k+1}-C_k=(\theta_{k+1}-\theta_k)S_k + (\eta_{k+1}-\eta_{k})$$

Where $S_k$ is the price of the risky asset at time $k$. Now I have a very simple question. If $\Delta C_{k+1}\le 0$, i.e. the costs over this time are negativ, does this mean, I gain something? What would this mean in reality? The bank/broker would give some money for buying/selling my risky asset or borrow/pay back money to the bank?

Where have you seen a negative transaction cost? For that matter, where did you see $\phi$, $\theta$, $\eta$? What are these? How does someone model a bank account? – chrisaycock Oct 3 '12 at 12:50
@chrisaycock I'm studying math. Usually you assume that the strategy is self-financing, i.e. $\Delta C_{k+1}=0$. But I want to know what the economical interpretation of a negative cost is. It's a general question and does not depend on $\phi,\theta,\eta$. It's a purely mathematical formulation and I want to know the economical interpretation of it. – hulik Oct 3 '12 at 12:54
@FKaria hulik doesn't say about negative hedging cost. $\Delta C_{k+1}\le 0$ doesn't mean negative hedging costs. It means that cost process is decreasing. – Alexey Kalmykov Oct 5 '12 at 11:46