of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale … similar to the optional decomposition. Furthermore, we prove an optional sampling theorem for the nonlinear martingale and …

This paper considers the nonlinear theory of G-martingales as introduced by Peng in [16, 17]. A martingale …

equivalent sigma-martingale measure for the price process, and the equivalence of no arbitrage of the fi rst kind to the … existence of an equivalent local martingale deflator for the set of non negative wealth processes …

decomposed into a sum with two opportunity processes L± appearing as coefficients. The martingale optimality principle translates …, stochastic control ; semimartingales ; BSDEs ; martingale optimality principle ; opportunity process ; E-martingales ; linear …

finance ; variance-optimal martingale measure …

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 … only a local integrability requirement. sigma-martingale ; equivalent martingale measures ; Jacod decomposition …

martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed … given, fi xed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value … of the option over all martingale measures that has the given marginal at maturity. In addition to duality, a family of …

deterministic function up to a random time γ at which they jump and stay constant afterwards. The (local) martingale properties of … application, we provide a construction of a (uniformly integrable) martingale M and a bounded (deterministic) integrand H such … that the stochastic integral H • M is a strict local martingale. Moreover, we characterise all local martingale deflators …