Related papers: Trajectory Based Models, Arbitrage and Continuity

This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price…

The goal of this paper is to prove a result conjectured in F\"ollmer and Schachermayer [FS07], even in slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular…

We prove that, for locally bounded processes, absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of…

We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds of a financial derivative. On top of marginal and martingale constraints, we introduce a time-homogeneity assumption,…

We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…

We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No…

The existence of time-lagged cross-correlations between the returns of a pair of assets, which is known as the lead-lag relationship, is a well-known stylized fact in financial econometrics. Recently some continuous-time models have been…

We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…

In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy. We make mild compactness assumptions but no…

In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…

We obtain a constructive criterion for robust no-arbitrage in discrete-time market models with transaction costs. This criterion is expressed in terms of the supports of the regular conditional upper distributions of the solvency cones. We…

This paper introduces a car following model where the driving scheme takes into account the deficiencies of human decision making in a general way. Aditionally, it improves certain shortcomings of most of the models currently in use: it is…

This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded…

The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely…

In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the…

Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…

We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most…

This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine…

We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading…

In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a…