A stoic may be thought of as such a person; one sense of this word is “a person indifferent to pleasure or pain”. The whole story of the meaning of stoic is somewhat more involved. Wikipedia's article on stoicism explains many of the ins and outs. It mentions, for example, that
The ancient Stoics are often misunderstood because the terms they used pertained to different concepts in the past than they do today. The word ‘stoic’ has come to mean ‘unemotional’ or indifferent to pain, because Stoic ethics taught freedom from ‘passion’ by following ‘reason.’ The Stoics did not seek to extinguish emotions; rather, they sought to transform them by a resolute ‘askēsis’ that enables a person to develop clear judgment and inner calm. ... The idea was to be free of suffering through apatheia ... or peace of mind ... Philosophy for a Stoic is not just a set of beliefs or ethical claims, it is a way of life involving constant practice and training (or askesis, see asceticism).
Note, while asceticism often entails “a lifestyle characterized by abstinence from various worldly pleasures”, it does not necessarily entail indifference to pleasure or pain, so asceticism by itself does not serve as a proper answer to the question.