zbMATH — the first resource for mathematics

Martingale and duality methods for utility maximization in an incomplete market. (English) Zbl 0733.93085
Let $$X^{x,\pi}$$ denote the wealth process corresponding to a portfolio $$\pi$$. $$X^{x,\pi}$$ is a solution of a linear Ito equation with $$X^{x,\pi}(0)=x.$$ The stochastic control problem is the following: To maximize the expected utility from terminal wealth $$EU(X^{s,\pi}(T))$$. 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:
 93E20 Optimal stochastic control 60G44 Martingales with continuous parameter 91B62 Economic growth models 49K45 Optimality conditions for problems involving randomness
Full Text: