I can understand why you put it the way you did then,
Milena. Most of the time, the distinction between
stative verbs and
activity verbs is pretty straight forward and not hard to make. Verbs like (
be)*, (
appear), (
see), (
think), (
know), (
believe), (
feel), (
resemble), (
wish), and others, seem to describe a stable situation that does not have a well-defined beginning or end (or at least, the beginning or end point is of no importance to the user). I guess that's why they are called "
states."
*I put verbs in brackets () to show that I mean all forms of the verb, such as
be, is, are, was, were, been, and so on.
But I always feel that grammatical characteristics like these do not inhere in the words themselves, but in the way they are used. For example, (
think) is usually thought of as a stative verb, presumably because we all (well most of us, anyway

) think more or less continuously. It's an ongoing
state. However, it is entirely possible (and correct) for someone to say, upon being asked whether she will join the group for a trip to the countryside this weekend:
"Well, I'm thinking maybe I'd better stay here and study for my English exam."
Now, you see, this use of (
think) is much more like an activity verb. The use of continuous form (not usually considered proper with stative verbs) implies that the activity described has a duration which is temporary--meaning that it has a beginning and an end which surely makes it look like an activity. Such a sentence would be not the least bit unusual to hear on a college campus, for instance. So, in my view at least, whether or not a verb is stative or activity in nature depends on how it is used. The verb (
live) is, I think, usually considered to be an activity verb, for what that's worth. In the use that you have presented, some variant of, "He lives in Geneva.", it can be presumed that he started to live there at some point in time, and continued to live there for some period of time which eventually, of course, must come to an end, either by his moving elsewhere or by his death.
The bottom line in the case of the two sentences you originally presented, however, Milena, is that both are correct sentences.
I wish you the best and hope this was helpful to you, at least a little.
Larry Latham