A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper explores anticipative binary information in financial markets using Brownian motion and Poisson processes.
Study shows Skorokhod insider outperforms forward insider in logarithmic utility maximization.
Study compares different integrals for optimal portfolio optimization with insider information.
New approach avoids restrictive assumptions for optimal portfolio in default risk scenarios.
Derives functional Itô formula for non-anticipative maps of rough paths.
We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Alòs in [2] for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used are non anticipative. …
Study optimal portfolios for traders with asymmetric information and delay.
Study on implied volatility of Asian options with stochastic volatility.
The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.
Study on implied volatility of Inverse options under stochastic volatility models.
The paper examines how markets can anticipate and react to arbitrage opportunities, revealing biases and risks.
Investigates invariant hulls of functionals on manifolds.
Various neural network based methods are capable of anticipating human body motions from data for a short period of time. What these methods lack are the interpretability and explainability of the network and its results. We propose to use Dynamic Mode Decomposition with delays to represent and anticipate human body mo…
Honest traders can outperform insiders in a Black-Scholes market with positive probability.
We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modelled via a counting process in line with large p…
Proves existence and trapped surface formation for Einstein-Vlasov system without symmetry assumptions.
Anticipatory portfolios use richer models to optimize investments.
Trading algorithms that execute large orders are susceptible to exploitation by order anticipation strategies. This paper studies the influence of order anticipation strategies in a multi-investor model of optimal execution under transient price impact. Existence and uniqueness of a Nash equilibrium is established unde…
We find prominent similarities in the features of the time series for the overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observations.
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 probabilistic notions. Our purely analytic framework allows for the derivation of a path…
AntLer anticipates future learning to improve control performance.
Corrects an earlier theorem, establishing new facts about information structures and non-anticipative aggregation.
Model predicts COVID-19 growth in Senegal, highlighting health care capacity importance.
Study embedding calculus and link invariants using functor calculus.
Most sales applications are characterized by competition and limited demand information. For successful pricing strategies, frequent price adjustments as well as anticipation of market dynamics are crucial. Both effects are challenging as competitive markets are complex and computations of optimized pricing adjustments…
Recurrent Neural Networks (RNNS) are now widely used on sequence generation tasks due to their ability to learn long-range dependencies and to generate sequences of arbitrary length. However, their left-to-right generation procedure only allows a limited control from a potential user which makes them unsuitable for int…
Embedding calculus proves convergence for surfaces.
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher order theory naturally involves higher algebra (n-fold groupoids).(conceptual, topol…
Secondary Calculus formalizes PDEs using cohomology, simplifying their study.
In arXiv:1207.0332 [cs.LO] was proposed a graphic lambda calculus formalism, which has sectors corresponding to untyped lambda calculus and emergent algebras. Here we explore the sector covering knot diagrams, which are constructed as macros over the graphic lambda calculus.
Machine learning and AI-assisted trading have attracted growing interest for the past few years. Here, we use this approach to test the hypothesis that the inefficiency of the cryptocurrency market can be exploited to generate abnormal profits. We analyse daily data for cryptocurrencies for the period between N…
Extends differential calculus to triole algebras.
Introduces tractors for basic examples and modern differential calculus.
A diagrammatic language for 3D manifolds with boundary.
Unified Lie structures in homotopy and isotopy calculus.
Behavior of systems that are functions of anticipated behavior of other systems, whose own behavior is also anticipatory but homeostatic and determined by hierarchical ordering, which changes over time, of sets of possible environments that are not co-possible, is proven to be highly non-linear and sensitively dependen…
We examine the N-Koszul calculus for the N-symmetric algebras. The case N=2 corresponds to the Elie Cartan calculus. We conjecture that, as in the case N=2, the N-Cartan calculus extends to manifolds when N>2, which would provide a new type of noncommutative differential geometry.
This paper is concerned with pseudodifferential calculus on manifolds with fibred corners. Following work of Connes, Monthubert, Skandalis and Androulidakis, we associate to every manifold with fibred corners a longitudinally smooth groupoid which algebraic and differential structure is explicitely described. This grou…
This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, or Heisenberg calculus. The Heisenberg manifolds generalize CR and contact manifolds and in this context the main differential operators at stake include the Hörmander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian and its conf…
Simplified calculus for semimartingales makes complex transformations easier.
Euler calculus is based on integrating simple functions with respect to the Euler characteristic. This paper makes the case for extending Euler calculus to continuous integrands by integrating with respect to (Gaussian) curvature. This requires a metric but is nevertheless defined within any O-minimal theory. It satisf…
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move…
Develops symmetric Cartan calculus linking to Patterson-Walker metric.
New algebraic formalism for differential calculus in Diolic algebras.
New calculus solves boundary value problems for elliptic operators.
New integration theory on topological spaces, including fractals.
Following the programme set out in Part I of this work, we develop a conceptual higher order differential calculus. The '' local linear algebra '' defined in Part I is generalized by '' higher order local linear algebra ''. The underlying combinatorial object of such higher algebra is the natural n-dimensional hyper-cu…