We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterise its three coefficient processes as solutions of...

We propose a simplified approach to mean-variance portfolio problems by changingtheir parametrisation from trading strategies to final positions. This allows us to treat,under a very mild no-arbitrage-type assumption, a whole range of quadratic optimisationproblems by simple mathematical tools...

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....

For an investor with constant absolute risk aversion and a long horizon, who trades in amarket with constant investment opportunities and small proportional transaction costs, weobtain explicitly the optimal investment policy, its implied welfare, liquidity premium, andtrading volume. We...

In a market with one safe and one risky asset, an investor with a long horizon, constantinvestment opportunities, and constant relative risk aversion trades with small proportionaltransaction costs. We derive explicit formulas for the optimal investment policy, its impliedwelfare, liquidity...

We provide a representation for the nonmyopic optimal portfolio of an agentconsuming only at the terminal horizon when the single state variable follows ageneral diusion process and the market consists of one risky asset and a risk-freeasset. The key term of our representation is a new object...

It is well known that non-normality plays an important role in asset and risk management.However, handling a large number of assets has long been a challenge.In this paper, we present a statistical technique that extends Principal ComponentAnalysis to higher moments such as skewness and...

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...