Ioannis Karatzas

TL;DR: In this paper, the valuation theory for American Contingent Claims is extended to deal with constraints on portfolio choice, including incomplete markets and borrowing/short-selling constraints, or with different interest rates for borrowing and lending.

TL;DR: In this paper, the authors generalized Fernholz and Karatzas' functional portfolio generation to a pathwise, probability-free setting, where the current market weights are replaced by path-dependent functionals, which involve the market weights, as well as additional bounded-variation functions of past and present market weights.

Abstract: Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently developed another methodology for the functional construction of portfolios, which leads to very simple conditions for strong relative arbitrage with respect to the market. In this paper, both of these notions of functional portfolio generation are generalized in a pathwise, probability-free setting; portfolio generating functions are substituted by path-dependent functionals, which involve the current market weights, as well as additional bounded-variation functions of past and present market weights. This generalization leads to a wider class of functionally-generated portfolios than was heretofore possible, and yields improved conditions for outperforming the market portfolio over suitable time-horizons.

TL;DR: In this paper, the Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimecorder on an enlarged probability space according to the excursion-theoretic methodology.

TL;DR: Ichiba et al. as discussed by the authors study systems of three interacting particles, in which drifts and variances are assigned by rank, and they study the stability properties for the resulting planar process of gaps between successive ranks.