ИСТИНА

Utility maximization problem is a classical problem in mathematical finance. From mathematical point of view, it is a class of problems dealing with an optimal control of stochastic processes. To solve it, dual methods are often used. In the talk we shall discuss how to state a dual problem and to establish dual relations. Such a problem can be formulated in abstract terms and refers essentially to functional analysis. Schematically, the solution of the problem consists of three steps: 1) to reduce an original problem to a similar one in appropriate functional spaces, e.g. $L^\infty$ (maybe, with a weight function), or Orlicz spaces with respect to a family of measures; 2) to state a dual problem using duality theorems; 3) to get rid of singular functionals in the dual problem.