| We study the problem of optimal investment in a general semimartingale financial market where risk, measured via coherent risk measures, is bounded. Two risk management policies are considered. The first one is dynamic. It follows a practitioner's approach, where the number of shares is assumed constant in the risk analysis. The problem turns out to be the classical optimal investment problem with constraints in the proportions of capital invested in each asset. It is solved in a general semimartingale setting using the duality approach and the optional decomposition of capital under constraints. The second risk management policy leads to a static problem; it is cast as a general optimization problem and tools from convex analysis and the theory of optimal investment are extended in order to obtain a duality based solution. Under our choice of coherent risk measures, both problems are convex. |
