Let S be an Rd-valued semimartingale and ( n) a sequence of C-valued inte-grands, i.e., predictable, S-integrable processes taking values in some given closedset C(!, t) ⊆ Rd which may depend on the state ! and time t in a predictable way.Suppose that the stochastic integrals ( n · S)...

Consider an Rd-valued semimartingale S and a sequence of Rd-valuedS-integrable predictable processes Hn valued in some closed convex set K C Rd,containing the origin. Suppose that the real-valued sequence Hn * S converges toX in the semimartingale topology.[...]

The Markowitz problem consists of finding in a financial market a self-financingtrading strategy whose final wealth has maximal mean and minimal variance. Westudy this in continuous time in a general semimartingale model and under coneconstraints: Trading strategies must take values in a...

We study mean-variance hedging under portfolio constraints in a general semi-martingale model. The constraints are formulated via predictable correspondences,meaning that the trading strategy is restricted to lie in a closed convex set whichmay depend on the state and time in a predictable way....

It is well known that mean-variance portfolio selection is a time-inconsistent optimalcontrol problem in the sense that it does not satisfy Bellman’s optimalityprinciple and therefore the usual dynamic programming approach fails. We developa time-consistent formulation of this problem, which...