Related papers: Limits of Semistatic Trading Strategies
In a two-period financial market where a stock is traded dynamically and European options at maturity are traded statically, we study the so-called martingale Schr\"odinger bridge Q*; that is, the minimal-entropy martingale measure among…
Semi-static trading strategies make frequent appearances in mathematical finance, where dynamic trading in a liquid asset is combined with static buy-and-hold positions in options on that asset. We show that the space of outcomes of such…
This is a survey of the basic results on the behavior of the number of the eigenvalues of a Schr\"odinger operator, lying below its essential spectrum. We discuss both fast decaying potentials, for which this behavior is semiclassical, and…
We compare the bottom of the spectrum of discrete and continuous Schr\"odinger operators with periodic potentials with barriers at the boundaries of their fundamental domains. Our results show that these energy levels coincide in the…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker…
Motivated by the connection between the Kyle equilibrium with static private signal and the Brownian bridge, we study a much broader class of bridges that allow one to consider more general equilibrium models, for example ones including…
We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework where a set of non-dominated models is given. The…
In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives.…
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
We introduce a new stochastic duration model for transaction times in asset markets. We argue that widely accepted rules for aggregating seemingly related trades mislead inference pertaining to durations between unrelated trades: while any…
We present several results concerning the semiclassical limit of the time dependent Schr\"odinger equation with potentials whose regularity doesn't guarantee the uniqueness of the underlying classical flow. Different topologies for the…
We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrodinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that both the exact and the numerical solutions…
This paper studies an optimal trading problem that incorporates the trader's market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by…
The theory of discrete periodic and limit-periodic Schr\"odinger operators is developed. In particular, the Floquet--Bloch decomposition is discussed. Furthermore, it is shown that an arbitrarily small potential can add a gap for even…
This work focuses on the well-posedness of abstract stochastic linear systems with boundary input delay and unbounded observation operators. We use product spaces and a semigroup approach to reformulate such delay systems into free-delay…
Whether you trade futures for yourself or a hedge fund, your strategy is counted. Long and short position limits make the number of unique strategies finite. Formulas of the numbers of strategies, transactions, do nothing actions are…
We prove that the spectrum of certain non-self-adjoint Schrodinger operators is unstable in the semi-classical limit. Similar results hold for a fixed operator in the high energy limit. The method involves the construction of approximate…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…