Martingale and duality methods for utility maximization in an incomplete market. (English) Zbl 0733.93085

Karatzas, Ioannis; Lehoczky, John P.; Shreve, Steven E.; Xu, Gan-Lin

SIAM J. Control Optimization 29, No. 3, 702-730 (1991).

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.

Reviewer: W.Grecksch (Merseburg)

MSC:

93E20	Optimal stochastic control
60G44	Martingales with continuous parameter
91B62	Economic growth models
49K45	Optimality conditions for problems involving randomness

Keywords:

stochastic control problem; Martingale techniques; convex optimization