ИСТИНА

The geometric approach to markets with proportional transaction cost prescribes to imbed a specific model (of stock market, of currency market etc.), usually given in a parametric form, into a natural framework defined by two processes, S and K. The first one, d-dimensional, models the price evolution of basic securities while the second one, cone-valued, describes the evolution of the solvency set. It happened that the fundamental questions --- no-arbitrage criteria, hedging problems, portfolio optimization --- can be studied in this general setting opening the door to set-valued techniques. In this talk we we discuss, in a such a general setting, the stochastic Mayer control problem, consisting in the maximization of expected utility of the portfolio terminal wealth. We provide some results on the continuity of the optimal value and the optimal control under price approximations. This is a joint work with Arthur Sidorenko.