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Martingale and duality methods for utility maximization in an incomplete market. (English) Zbl 0733.93085
Let X x,π denote the wealth process corresponding to a portfolio π. X x,π is a solution of a linear Ito equation with X x,π (0)=x· The stochastic control problem is the following: To maximize the expected utility from terminal wealth EU(X s,π (T)). This problem is an example of the utility maximization in an incomplete market containing a bound and a finite number of stocks. The prices are driven are driven by an n-dimensional Brownian motion W. The number of stocks is strictly smaller than the dimension of W. Martingale techniques and convex optimization are used.

MSC:
93E20Optimal stochastic control (systems)
60G44Martingales with continuous parameter
91B62Growth models in economics
49K45Optimal stochastic control (optimality conditions)