We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We obtain the duality of results for the sub- and...

We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need...

On a filtered probability space $(\Omega,\mathcal{F},P,\mathbb{F}=(\mathcal{F}_t)_{0\leq t\leq T})$, we consider stopper-stopper games $\bar C:=\inf_{\Rho}\sup_{\tau\in\T}\E[U(\Rho(\tau),\tau)]$ and $\underline C:=\sup_{\Tau}\inf_{\rho\in\T}\E[U(\Rho(\tau),\tau)]$ in continuous time, where...

We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with bid-ask spreads. In this set-up, we need to work with the...

We consider nonparametric prediction problem for both short- and long-range-dependent linear processes. Asymptotic properties of local linear estimates are obtained and, for long-range-dependent processes, an interesting dichotomous phenomenon is described: the limiting distribution depends on...

We consider the robust estimation of regression parameters in linear models with long memory and heavy-tailed errors. Asymptotic Bahadur-type representations of robust estimates are developed and their limiting distributions are obtained. It is shown that the limiting distributions are very...

The paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models. Using a Gaussian approximation result for non-stationary multiple time series, we show that the constructed simultaneous confidence tubes have asymptotically...

We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model to call options with discrete set of maturities but a...

We consider the robust utility maximization using a static holding in derivatives and a dynamic holding in the stock. There is no fixed model for the price of the stock but we consider a set of probability measures (models) which are not necessarily dominated by a fixed probability measure. By...