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...

Here, we study the case where the portfolio rebalancement involves the payment of taxes on benefits. Then, the purchasing time of the asset to be sold has to be recorded in order to compute the amount of tax to be paid. In addition to the no-short-selling constraint, our model assumes that sales...

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...