Related papers: No-Arbitrage Symmetries
We examine the properties of algebras of linear transformations that leave invariant all subspaces in a totally ordered lattice of subspaces of an arbitrary vector space. We compare our results with those that apply for the corresponding…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
We expand the class of linear symmetric equations for which large sets with no non-trivial solutions are known. Our idea is based on first finding a small set with no solutions and then enlarging it to arbitrary size using a…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are…
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…
Recent advances in nonequilibrium statistical mechanics shed new light on the ratchet effect. The ratchet motion can thus be understood in terms of symmetry (breaking) considerations. We introduce an additional symmetry operation besides…
An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and…
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash…
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…
We discuss the convergence problem for coordinate transformations which take a given vector field into Poincar\'e-Dulac normal form. We show that the presence of linear or nonlinear Lie point symmetries can guaranteee convergence of these…
The present work pursues the aim to draw attention to unique possibilities of the skew-symmetric differential forms. At present the theory of skew-symmetric exterior differential forms that possess invariant properties has been developed.…
The breaking of space-time symmetries and the non-conservation of the associated Noether charges constitutes a central artifact in lattice field theory. In prior work we have shown how to overcome this limitation for classical actions…
The gauge symmetry is said unfree if the gauge transformation leaves the action functional unchanged provided for the gauge parameters are constrained by the system of partial differential equations. The best known example of this…
We consider the one-factor model of commodities for which the parameters of the model depend upon the stock price or on the time. For that model we study the existence of group-invariant transformations. When the parameters are constant,…
We make an attempt to develop "noncommutative algebraic geometry" in which noncommutative affine schemes are in one-to-one correspondence with associative algebras. In the first part we discuss various aspects of smoothness in affine…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
In this work we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in $f(R,T)$ theory. Restricted axial symmetry ignoring rotation and reflection enteries is taken into account for…
Symmetries of both closed and open-system dynamics imply many significant constraints. These generally have instantiations in both classical and quantum dynamics (Noether's theorem, for instance, applies to both sorts of dynamics). We here…
We provide a Fundamental Theorem of Asset Pricing and a Superhedging Theorem for a model independent discrete time financial market with proportional transaction costs. We consider a probability-free version of the Robust No Arbitrage…