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A characterization of value efficiency.

Alfonso Mateos, Sixto Ríos-Insua (1996)

Extracta Mathematicae

An important issue in multi-attribute decision making consists of identifying the set of efficient solutions. The importance of this set is that the decision maker (DM) can restrict his attention to it, discarding all other solutions, because a nonefficient solution can never be optimal. Several methods have been developed to aid a DM in generating all or representative subsets of efficient solutions, [1] and [4], or to approximate it [7]. However most of these methods may be hard to apply to nonlinear...

Comparison principle approach to utility maximization

Peter Imkeller, Victor Nzengang (2015)

Banach Center Publications

We consider the problem of optimal investment for maximal expected utility in an incomplete market with trading strategies subject to closed constraints. Under the assumption that the underlying utility function has constant sign, we employ the comparison principle for BSDEs to construct a family of supermartingales leading to a necessary and sufficient condition for optimality. As a consequence, the value function is characterized as the initial value of a BSDE with Lipschitz growth.

Convergence of optimal strategies in a discrete time market with finite horizon

Rafał Kucharski (2006)

Applicationes Mathematicae

A discrete-time financial market model with finite time horizon is considered, together with a sequence of investors whose preferences are described by a convergent sequence of strictly increasing and strictly concave utility functions. Existence of unique optimal consumption-investment strategies as well as their convergence to the limit strategy is shown.

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