Related papers: No-Arbitrage Symmetries
Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On…
Left-right symmetric models are analyzed in the context of noncommutative geometry where we show that spontaneous parity violation is ruled out.
Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage…
This paper completes the analysis of Choulli et al. Non-Arbitrage up to Random Horizons and after Honest Times for Semimartingale Models and contains two principal contributions. The first contribution consists in providing and analysing…
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…
We prove a version of the fundamental theorem of asset pricing (FTAP) in continuous time that is based on the strict no-arbitrage condition and that is applicable to both frictionless markets and markets with proportional transaction costs.…
This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of…
Invariance properties of semimartingales on Lie groups under a family of random transformations are defined and investigated, generalizing the random rotations of the Brownian motion. A necessary and sufficient explicit condition…
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices…
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties…
The goal of this article is to understand some interesting features of sequences of arbitrage operations, which look relevant to various processes in Economics and Finances. In the second part of the paper, analysis of sequences of…
We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes…
In this paper we study arbitrage theory of financial markets in the absence of a num\'eraire both in discrete and continuous time. In our main results, we provide a generalization of the classical equivalence between no unbounded profits…
Motivated by applications to bond markets, we propose a multivariate framework for discrete time financial markets with proportional transaction costs and a countable infinite number of tradable assets. We show that the no-arbitrage of…
This paper is concerned with an optimal control problem for a nonhomogeneous linear stochastic differential equation having regime switching with a quadratic functional in the large time horizon. This is a continuation of the paper…
We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a…
Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes…
A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and…