This work gives a brief overview of the portfolio selection problem following the mean-risk approach first proposed by Markowitz (1952). We consider various risk measures, i.e. variance, value-at-risk and expected-shortfall and we study the efficient frontiers obtained by solving the portfolio...

Previous research has shown that frictions might have a significant impact on the value of a contingent claim, as discussed, for example, in Karatzas & Kou (1996)and Collin-Dufresne & Hugonnier (2002). We consider two types of frictions particularly important: frictions related to trading, such...

Arbitrage pricing cannot be applied to commodity futures because the physicalcommodity does not represent a pure asset: Since consumption and processing of thecommodity can drive down inventories to zero, it is not always possible to construct areplicating portfolio for the futures contract, and...