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.
Geodesic flows on surfaces have specific fractional-linear integrals related to constant cross-ratios.
The study provides a criterion for fractional-linear integrals of geodesics on surfaces.
Study extends convexity in curved spaces using fractional integrals.
Extends Young integral to Hölder differential forms in arbitrary dimensions.
A new method calculates fractional moments using the moment-generating function.
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical …
Using the fractional integration and differentiation on R we build the fractional jet fibre bundle on a differentiable manifold and we emphasize some important geometrical objects. Euler-Lagrange fractional equations are described. Some significant examples from mechanics and economics are presented.
The paper evaluates integrals for fBm with various Hurst indices.
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov fractional differences of non-integer order d. Equations of ARIMA(p,d,q) and ARFIMA(…
In this paper we established the condition for a curve to satisfy stochas- tic fractional HP (Hamilton-Pontryagin) equations. These equations are described using It^o integral. We have also considered the case of stochastic fractional Hamiltonian equa- tions, for a hyperregular Lagrange function. From the stochastic fr…
Develops fractional de Rham theory for Maxwell equations.
Paper introduces a new optimization method for imbalanced datasets.
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.
Research on unique continuation principles in medical and seismic imaging.
In this paper we provide an integral representation of the fractional Laplace-Beltrami operator for general riemannian manifolds which has several interesting applications. We give two different proofs, in two different scenarios, of essentially the same result. One of them deals with compact manifolds with or without …
We determine Kelly criterion for a game with variable pay-off. The Kelly fraction satisfies a fundamental integral equation and is smaller than the classical Kelly fraction for the same game with the constant average pay-off.
Enhances option pricing with fractional order Black-Scholes-Merton model.
This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate transformation rules for integral order forms are also computed. Matrix order f…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector spaces of finite and infinite dimension, fractional differential form spaces. The def…
Many fractional processes can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily high polynomial order. This explains the potential, but also s…
Study large deviations in fractional volatility models with non-Gaussian volatility.
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part, followed by a reasonable approximation we show that it is possible to cast the proble…
Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we…
Study connects weighted isoperimetric problems to nonlocal elliptic operator extensions.
New method combines long-memory reservoirs for accurate dengue forecasting from short data.
Study rough volatility models using path-dependent PDEs and fractional Brownian motions.
Develops nonparametric regression for non-smooth functions using fractional Laplacian.
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-kno…
G-framework is presented by Peng [41] for measure risk under uncertainty. In this paper, we define fractional G-Brownian motion (fGBm). Fractional G-Brownian motion is a centered G-Gaussian process with zero mean and stationary increments in the sense of sub-linearity with Hurst index . This process has sta…
Quantum probability theory constructs Martingales for non-Brownian financial models.
Accelerators with power-law memory are proposed in the framework of the discrete time approach. To describe discrete accelerators we use the capital stock adjustment principle, which has been suggested by Matthews.The suggested discrete accelerators with memory describe the economic processes with the power-law memory …
New rough stochastic volatility models using log-modulated fractional Brownian motion.
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial data, treating and discovering unknown equation parameters as hyperparameters of a…
New IBP formulae for rough stochastic Volterra processes.
There exists and is unique up to multiplication by a constant function a form of the highest dimension on the manifold of n-dimensional continued fractions in the sense of Klein, such that the form is invariant under the natural action of the group of projective transformations PGL(n+1). A measure corresponding to the …
Estimates roughness of volatility from discrete variance data.
We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stocha…
The study tackles rough noise in high-frequency financial data using fractional Brownian motion.
Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.
The paper models cryptocurrency price and volatility with jumps and fractional volatility.
Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations = $(1-\sum\limits_{j=1}^q β_j L^j)σ_{t}^2 = ω+(1-\sum\limits_{j=1}^q β_j L^j -…
The paper introduces a new stochastic volatility model with long-term memory and jumps.
We discuss several aspects of Mellin transform, including distributional Mellin transform and inversion of multiple Mellin-Barnes integrals in and its connection to residue expansion or evaluation of Laplace integrals. These mathematical concepts are demonstrated on several option-pricing models. This in…
Formula for option pricing in a stochastic volatility model with jumps.
Proposes a deep neural network for predicting survival times with cure fractions.
Develops a GMM method to estimate roughness in stochastic volatility models.
Paper extends a method to estimate Hurst parameter for rough stochastic volatility models.
SigMA uses signatures and attention to estimate parameters in fBm-driven SDEs.