Using optimal control without loss the money in future

Abstract

The purpose of writing this paper is to demonstrate a short study  to learn  how the person  to maximize his money  by using an optimal control without  loss. The purpose  of the control is to maximize the expected  payoff  in the future . We have in this paper very valuable result .

If we have found an optimal decision that will bring some positive inpute in future . We know that to maximize our money with out losing is actually  very necessary part in our life.

Suppose that the state  of a system  at time  t is described by ito process

of the form

Markov control is assume that  does not depend on the starting point  , the value we choose at time   only dependes on of the system at this time.