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.
Chebyshev technique reduces FRTB-IMA equity autocallables computation costs by 90%.
New technique reduces FRTB IMA capital calculation burden by over 90%.
Financial institutions now face the important challenge of having to do multiple portfolio revaluations for their risk computation. The list is almost endless: from XVAs to FRTB, stress testing programs, etc. These computations require from several hundred up to a few million revaluations. The cost of implementing thes…
IMA improves representation learning even when assumptions are violated.
IMA addresses non-identifiability in nonlinear ICA by assuming orthogonal Jacobian columns.
Facing the FRTB, banks need to allocate their capital to each business units or risk positions to evaluate the capital efficiency of their strategies. This paper proposes two computationally efficient allocation methods which are weighted according to liquidity horizon. Both methods provide more stable and less negativ…
We present a variation of the Autoencoder (AE) that explicitly maximizes the mutual information between the input data and the hidden representation. The proposed model, the InfoMax Autoencoder (IMAE), by construction is able to learn a robust representation and good prototypes of the data. IMAE is compared both theore…
In this work, we study robust deep learning against abnormal training data from the perspective of example weighting built in empirical loss functions, i.e., gradient magnitude with respect to logits, an angle that is not thoroughly studied so far. Consequently, we have two key findings: (1) Mean Absolute Error (MAE) D…
These notes are based on my lectures at IMA summer program "Symmetries and Overdetermined Systems of Partial Differential Equations." Here I try to explain basic ideas of the ambient metric construction by studying the Szego kernel of the sphere.
This work reviews and tests risk allocation strategies in finance, highlighting Shapley allocation's advantages.
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as detour complexes. This elaborates on a lecture given at the IMA Summer Programme ``S…
New SigSwap model for path-dependent financial risk.
Unified RMOT framework for non-modelable risk factors reduces audit bounds.
VAEs improve representation learning by inverting the data-generating process through self-consistency.
In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thomée (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally parallelizable. It is shown that the method is very efficient for calculating vari…
A reduction method of ODEs not possessing Lie point symmetries makes use of the so called -symmetries (C. Muriel and J. L. Romero, \emph{IMA J. Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE is used here to recover -symmetries of as nonlocal symmetries. In …
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parame…
This is an expanded version of a series of two lectures given at the IMA summer program "Symmetries and Overdetermined Systems of Partial Differential Equations". The main part of the article describes the Riemannian version of the prolongation procedure for certain overdetermined system obtained recently in joint work…
MPANF improves naive forecast by incorporating directional information.
Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that backtesting of expected shortfall - or the trading book model from which it is calcula…
An Ensemble Anomaly Detection Framework for Risk Calculation Integrity
Differential ML combines AAD with ML for fast, accurate financial derivatives pricing and risk management.
SHARC explains machine learning risk models for regulatory capital, linking outputs to scenarios.
New step-size methods improve SHB convergence for stochastic optimization.