We define (d,n)-coherent risk measures as set-valued maps from <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$L^\infty_d$</EquationSource> </InlineEquation> into <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\mathbb{R}^n$</EquationSource> </InlineEquation> satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the...</equationsource></inlineequation></equationsource></inlineequation>

We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random...

We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random...

We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random...

The purpose of the paper is to introduce a tighter definition for the marginal pricing rule. By means of an example, we illustrate the improvements that one gets with the new definition with respect to the former one with the Clarke's normal come.

In this paper, we present a more simple and independent proof of Reny's theorem (1998), on the existence of a Nash equilibrium in discontinue game, with a better-reply secure game in a Hausdorff topological vector space stronger than Reny's one. We will get the equivalence if the payoff function...