After signing the lease, the tenant owes you for 12 months rent if they moved out after 1 day. Regarding the security deposit, yes- keep it.
The landlord may only keep a security deposit for three things: 1. To cover unpaid rent.
2. To repair anything the tenant damaged, other than from ordinary wear and tear.
3. To pay for rent if the tenant moves out without giving proper notice. However, the landlord must try to find a new tenant, and as soon as there is a new tenant in your apartment he can no longer charge you rent.