Optimum Savings and Utility Maximization Over Time

Utility Maximization and Duality

In an arbitrage free incomplete market we consider the problem of maximizing terminal isoelastic utility. The relationship between the optimal portfolio, the optimal martingale measure in the dual problem and the optimal value function of the problem is described by an BSDE. For a totally unhedgeable price for instantaneous risk, isoelastic utility of terminal wealth can be maximized using a po...

Anomalies: Utility Maximization and Experienced Utility

Implicit Maximization of Flows over Time

Flows over time may be maximized by computing a static maximum flow on the corresponding time-expanded network, which contains a copy of the original network for each discrete time step. This makes available the whole algorithmic toolbox developed for static flows. The major drawback of this method compared to a polynomial (motivated by Ford and Fulkerson [6, 7]) is that the time-expanded netwo...

Utility Maximization under Uncertainty

Motivated by several search and optimization problems over uncertain datasets, we study the stochastic versions of a broad class of combinatorial problems where either the existences or the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees, and minimum weight matchings over probabilistic graphs;...

Expected Qualitative Utility Maximization

A model for decision making that generalizes Expected Utility Maximization is presented. This model, Expected Qualitative Utility Maximization, encompasses the Maximin criterion. It relaxes both the Independence and the Continuity postulates. Its main ingredient is the definition of a qualitative order on nonstandard models of the real numbers and the consideration of nonstandard utilities. Exp...