Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure P is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local P-martingales. We...

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

An equivalent sigma-martingale measure (EsigmaMM) for a given stochastic process S is a probability measure R equivalent to the original measure P such that S is an R-sigma-martingale. Existence of an EsigmaMM is equivalent to a classical absence-of-arbitrage property of S, and is invariant if...

In general multi-asset models of financial markets, the classic no-arbitrage concepts NFLVR and NUPBR have the serious shortcoming that they depend crucially on the way prices are discounted. To avoid this economically unnatural behaviour, we introduce a new way of defining “absence of...

We study general undiscounted asset price processes, which are only assumed to be non- negative, adapted and RCLL (but not a priori semimartingales). Traders are allowed to use simple (piecewise constant) strategies. We prove that under a discounting-invariant condition of absence of arbitrage,...

For a large financial market (which is a sequence of usual, “small” financial markets), we introduce and study a concept of no asymptotic arbitrage (of the first kind) which is invariant under discounting. We give two dual characterisations of this property in terms of (1) martingale-like...