arXiv research

We analyze the semi-hard triplet loss using Edgeworth expansion for better understanding of its behavior.

We derive a higher-order expansion for rough volatility models.

New insights on pruning deep networks by preserving function locality.

Paper develops formulas for shape derivatives in wave scattering.

Expanding the rough Heston model in $H$

We obtain a first order extension of the large deviation estimates in the Gärtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order one to that of the original family of measures. The construction of the special fam…

We develop closed-form approximations for European put options under stochastic volatility models.

Validates replica trick for simple models using replica analytic continuation.

We consider a financial market with liquidity cost as in Çetin, Jarrow and Protter [2004], where the supply function $S^ε(s,ν)$ depends on a parameter $ε\geq 0$ with $S^0(s,ν)=s$ corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi [2010] of the super-hedging cost of a…

It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment $s_+$ can be obtained by solving (numerically) a simple equation. This yields a leading order expansion for the implied volatility at large strikes: $σ_{BS}( k,T)^{2}T\sim Ψ(s_+-1) \times k$ (Roger Lee's moment…

Study proposes a method to construct copulas using corrected Hermite polynomial expansion for estimating foreign exchange volatility.

In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of …

We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kern…

Study on neural networks' performance under different normalizations as N grows.

We develop a first order expansion for convex penalized estimators in high-dimensional regression.

Study improves BN TTA under distribution shift using higher-order asymptotics.

Develops a new framework to analyze gradient flow regimes and derive explicit solutions.

RPN unifies various models with a reconciled polynomial network.

A third-order approximation for close-to-the-money European option prices under an infinite-variation CGMY Lévy model is derived, and is then extended to a model with an additional independent Brownian component. The asymptotic regime considered, in which the strike is made to converge to the spot stock price as the ma…

This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distri…

Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we…

Efficiently calibrates Libor Market Model with SV-DD using Edgeworth expansions.

Paper proves vanishing terms in a second Poisson bracket for a specific system.

Unified framework for adaptive learning systems using consolidation and expansion operations.

A new machine learning method uses stochastic functions to predict data with optimized few parameters.

Cumulant expansion is used to derive accurate closed-form approximation for Monthly Sum Options in case of constant volatility model. Payoff of Monthly Sum Option is based on sum of $N$ caped (and probably floored) returns. It is noticed, that $1/\sqrt{N}$ can be used as a small parameter in Edgeworth expansion. First …

The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing high-order asymptotic expansions for the at-the-money implied volatility skew, under a…

We approximate prices of various financial claims using a combination of expansions.

The volume conjecture is extended to all orders for hyperbolic 3-manifolds using complex Chern-Simons theory.

Deep neural network solves portfolio optimization with MGARCH and small transaction costs.

New formulas for pricing Asian and basket options using stochastic expansion.

The paper develops an expansion for optimizing portfolios with small quadratic transaction costs.

Develops a martingale expansion for stochastic volatility models.

Polynomial time algorithm learns depth-2 neural networks with ReLU activations.

Taylor expansions improve reinforcement learning policies.

Sparse random features improve accuracy in data-scarce settings.

Investor optimizes wealth in a market with non-traded endowment, deriving expansions up to second order.

Bayesian optimization tackles unknown search spaces with automatic expansion.

Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.

The paper calculates heat kernel and closed geodesic asymptotics for nilpotent coverings.

Paper tackles high-order inference in structured prediction tasks.

The paper provides non-asymptotic Edgeworth expansions for neural network outputs.

Study local expansions of continuous-time processes using Ito signature properties.

Paper prices geometric Asian options using a multifactor stochastic volatility model.

We establish multiparameter resolvent trace expansions for elliptic boundary value problems, polyhomogeneous both in the resolvent and the auxiliary parameter. The present analysis is rooted in the joint project with Matthias Lesch on multiparameter resolvent trace expansions on revolution surfaces with applications to…

In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in R^n up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and frontal deviation for surfaces in R^3. Also we compute, by using the Taylor expan…

Study evaluates methods for expanding communities in hypergraphs using random walks.

The study improves volatility model pricing accuracy with new statistical expansions.