new landlord/"new property" low rents and no security deposit

[Bryan Mills]

New investor here "closed today" on a duplex...YAY!!!  I want to make sure I am taking the correct steps. Current tenants have low rents and seller did not require a security deposit. To cover my butt I realize I need to obtain a security deposit and increase the rents. One tenant has lived in one side of the property for 30 years (very low rent) the other for nearly 10 years (close to market rates). Seller says both tenants have been great so I would hate to loose them bc their security deposit would make their monthly july rent double. The property does make a minimal monthly profit but not near market rate.  

excuse: I also teach school, coach and of course limited funds... so time is limited in updating the property and finding new tenants could be challenging if tenants would decide to move. Would love some suggestions:

1.  Raise the rent to market, require a security deposit take my chance on losing the tenants?

2.  Slightly raise rents require a security deposit? 

3.  Leave rents where they are require a security deposit and hope tenants stay for another year? 

30 years in one spot...makes this decision a little difficult. Yes I want to be a savvy investor but not a total jerk either.  ANY suggestions would be GREAT!!!

Thank you,

Bryan