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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)
We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process follows a general martingale. This is equivalent to studying the rst centered absolute moment of. We show that if has a continuous part, the leading term is of order √ in time and depends only on the initial value of the volatility.(More)
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)
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)
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)