Sara Biagini

On the extension of the Namioka-Klee theorem and on the Fatou property for Risk Measures

This paper has been motivated by general considerations on the topic of Risk Measures, which essentially are convex monotone maps defined on spaces of random variables, possibly with the so-called Fatou property.

Utility maximization in incomplete markets for unbounded processes

Abstract.When the price processes of the financial assets are described by possibly unbounded semimartingales, the classical concept of admissible trading strategies may lead to a trivial utility maximization problem because the set of stochastic integrals bounded from below may be reduced to the zero process. However, it could happen that the investor is willing to trade in such a risky market, where potential losses are unlimited, in order to increase his/her expected utility. We translate this attitude into mathematical terms by employing a class

A Unified Framework for Utility Maximization Problems: an Orlicz space approach

\mathcal{H}^{W}

Robust Fundamental Theorem for Continuous Processes

of W-admissible trading strategies which depend on a loss random variable W. These strategies enjoy good mathematical properties and the losses they could generate in trading are compatible with the preferences of the agent.We formulate and analyze by duality methods the utility maximization problem on the new domain

The supermartingale property of the optimal wealth process for general semimartingales

\mathcal{H}^{W}

An Orlicz Spaces Duality for Utility Maximization in Incomplete Markets

. We show that, for all loss variables W contained in a properly identified set

Dynamic quasi-concave performance measures

\mathcal{W}

Model-Free Representation of Pricing Rules as Conditional Expectations

, the optimal value on the class

The Best Gain-Loss Ratio is a Poor Performance Measure

\mathcal{H}^{W}

RELAXED UTILITY MAXIMIZATION IN COMPLETE MARKETS

is constant and coincides with the optimal value of the maximization problem over a larger domain