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- Marcel Nutz
- 2012

We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Path-by-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial limit coincides with the usual stochastic integral under essentially any probability measure such that… (More)

- Marcel Nutz, Eth Zurich
- 2010

We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a novel transformation of the model to avoid… (More)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the martingale inequality is determined by a fixed point of a… (More)

- Bruno Bouchard, Marcel Nutz
- 2013

We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures. In the arbitrage-free case, we show… (More)

- Marcel Nutz, Eth Zurich, Martin Schweizer, Nicholas
- 2009

We study utility maximization for power utility random elds with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in terms of the opportunity process, which is… (More)

- Marcel Nutz, Ramon Van Handel
- 2013

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random-expectation, and an optional sampling theorem that holds without exceptional set. Our results… (More)

- Ariel Neufeld, Marcel Nutz
- 2013

We establish the duality formula for the superreplication price in a setting of volatility uncertainty which includes the example of random-expectation. In contrast to previous results, the contingent claim is not assumed to be quasi-continuous. 1 Introduction This paper is concerned with superreplication-pricing in a setting of volatility uncertainty. We… (More)

- Marcel Nutz, Eth Zurich
- 2010

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to innity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The… (More)

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strategy is obtained from a representation… (More)

- Marcel Nutz
- ArXiv
- 2011

We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This value process is characterized by a second… (More)