How do we solve optimization problems with infinite horizon. I tried to look online for some guidance but nothing but just problems and no solution methods. For example how can I solve: maximize a_t [itex]\in[/itex][0,1] [itex]\sum\frac{-2a_t}{3}[/itex]+log(S_T) where sum goes from 0 to T-1 subject to: s_t+1 = s_t *(1+a_t) Some sources say we can use backwards induction but doesn't really tell me how I can do so. Can someone explain the methodology or direct me to somewhere that explains it. Thanks