All perfect praise be to Allah, The Lord of The Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
It is permissible to raise dogs and teach them how to hunt and guard property in addition to serve other lawful purposes because it was reported in Sahih Bukhari and Sahih Muslim that the Prophet(PBUH) said: "If somebody keeps a dog that is neither used for farm work nor for guarding the livestock, he will lose one Qirat (of the reward) of his good deeds every day."{Agreed upon}. Al-Khateeb Ash-Shirbini(May Allah have mercy on him) stated: "As it is permissible to keep a dog to use it for hunting as well as guarding livestock, then it is permissible to raise a puppy to use it as such."{Moghni Al-Mohtajj, 2/342}.
However, Muslim scholars have disagreed as regards selling and buying dogs. Some of them prohibited that; whereas, the Hanafi and Maliki scholars-in one opinion-permitted it, saying that the prohibition pertains to dogs that people aren`t permitted to keep.
Moreover, Islam has permitted training and teaching dogs since Allah, The Almighty, said in this regard: " They ask thee what is lawful to them (as food). Say: lawful unto you are (all) things good and pure: and what ye have taught your trained hunting animals (to catch) in the manner directed to you by Allah. eat what they catch for you, but pronounce the name of Allah over it: and fear Allah. for Allah is swift in taking account."{Al-Mai`dah/4}.
Nonetheless, training is a key condition to consider what these dogs hunt as lawful food, but if they are kept for ornament and trading, then it is neither permissible to keep them nor to sell and buy them. And Allah knows best.