We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our...

The importance of portfolio optimization in finance field has been increasing significantly. Although, portfolio optimization problems over a single period or multiple periods are studied extensively, the problem with an option to rebalance over multiple periods is not considered significantly....

We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization...

We consider the problem of optimizing a portfolio of n assets, whose returns are described by a joint discrete distribution. We formulate the mean-risk model, using as risk functionals the semideviation, deviation from quantile, and spectral risk measures. Using the modern theory of measures of...

We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk...