Mathematical definition of a hedge?

For two given portfolios/trading strategies I want to know what criteria need to fulfilled in order to call the one portfolio a hedge to the other. In other words; what is the mathematical definition of a hedge given in terms of the value processes of the portfolios? before down voting this question for being to basic please google ‘hedge definition’ and the first many hits won’t give you an mathematical definition but rather oral explanations. Thanks

• It sure seems like everyone wants to define hedging by examples and oral explanations. There must be some quant who has given a mathematical definition – user32091 Mar 3 '18 at 21:55
• This should and will get voted down though. Please google “mathematics of hedging”. – Ivan Mar 3 '18 at 22:35
• I agree that the question is "too" basic yet the author is right when he/she claims that it's actually not easy to find through what the mathematical definition is. I had to look it up in a book. – Sanjay Mar 3 '18 at 23:17

If you have a T-claim $X$, then $h$ is a hedge portfolio if and only if $h$ is self-financing and the value $V^h(t)$ at time $T$ is as following: $$V^h(T)=X$$