Related papers: Ramification of Volterra-type Rough Paths
In the paper regularity of solutions to stochastic Volterra equations in a separable Hilbert space is studied. Sufficient conditions for the temporal and spatial regularity of stochastic convolutions corresponding to the equations under…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
In the paper, we improve our earlier results concerning the existence, uniqueness and differentiability of a global implicit function. Some application to a Cauchy problem for an integro-differential Volterra system of nonconvolution type,…
We introduce a novel simulation scheme, iVi (integrated Volterra implicit), for integrated Volterra square-root processes and Volterra Heston models based on the Inverse Gaussian distribution. The scheme is designed to handle $L^1$ kernels…
Well-known operations defined on a non-degenerate inner product vector space are extended to the case of a degenerate inner product. The main obstructions to the extension of these operations to the degenerate case are (1) the index…
In this work the path integral formulation for rigid rotors, proposed by M\"user and Berne [Phys. Rev. Lett. {\bf 77}, 2638 (1996)], is described in detail. It is shown how this formulation can be used to perform Monte Carlo simulations of…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…
In this paper, we consider equilibrium strategies under Volterra processes and time-inconsistent preferences embracing mean-variance portfolio selection (MVP). Using a functional It\^o calculus approach, we overcome the non-Markovian and…
We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on F{\"o}llmer…
In this complementary note to [1] (arXiv:1501.05641), we provide an alternative proof for the factorial decay estimate of iterated integrals for geometric rough paths without using the neoclassical inequality. This note intends to aid the…
We prove a complexity dichotomy theorem for Holant Problems on 3-regular graphs with an arbitrary complex-valued edge function. Three new techniques are introduced: (1) higher dimensional iterations in interpolation; (2) Eigenvalue Shifted…
We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field. Existing decomposition methods impose constraints on the behavior of vector fields at infinity and require…
This paper focuses on the study of integro-differential equations with delays, presenting a novel perturbation approach. The primary objective is to introduce the concepts of classical and mild solutions for these equations and establish…
We introduce tools from numerical analysis and high dimensional probability for precision control and complexity analysis of subdivision-based algorithms in computational geometry. We combine these tools with the continuous amortization…
We develop a variant of rough path theory tailor-made for analyzing a class of financial asset price models known as rough volatility models. As an application, we prove a pathwise large deviation principle (LDP) for a certain class of…
Singular stochastic partial differential equations informally refer to the partial differential equations with rough random force that leads to the products in the nonlinear terms becoming ill-defined. Besides the theories of regularity…