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...

An equivalent !-martingale measure (E!MM) for a given stochastic process Sis a probability measure R equivalent to the original measure P such that S isan R-!-martingale. Existence of an E!MM is equivalent to a classical absenceof-arbitrage property of S, and is invariant if we replace the...

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

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....

The well-known absence-of-arbitrage condition NFLVR from the fundamentaltheorem of asset pricing splits into two conditions, called NA and NUPBR.We give a literature overview of several equivalent reformulations of NUPBR;these include existence of a growth-optimal portfolio, existence of the...

We introduce and study no-good-deal valuation bounds defined in terms of expected utility. A utility-based good deal is a payoff whose expected utility is toohigh in comparison to the utility of its price. Forbidding good deals induces, viaduality, restrictions on pricing kernels and thereby...

We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and...