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.
Paper uses Chebyshev Tensors for accurate dynamic sensitivities and ISDA SIMM computation.
This work reduces DIM computation costs by training neural networks on single MC paths.
We present two methods, based on Chebyshev tensors, to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation. These methods are implemented and run in a Monte Carlo engine to compute Dynamic Initial Margin as defined by ISDA (SIMM). We show that the levels of accuracy, speed and impleme…
The paper tackles fVaR prediction methods in finance.
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an initial condition and view the problem as a stochastic control problem; we esta…
Paper improves ISDA margin calculation using LSMC.
In a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inequality. Namely, as discussed in the paper, its area must be bounded above by , where is a lower bound on a natural energy-momentum term. We then consider th…
Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg 2010, Piterbarg2012), under counterparty risk with unsecured funding costs (FVA) (Burgard2011, Burgard2011, Burgard2013) and in the presence of re…
Constructs initial data leading to apparent horizons and tests Penrose Inequality.
AIS uses a suboptimal extended target distribution, which this paper improves using SGM.
Proposes a method to optimize neural network initialization using marginal likelihood maximization.
New MKABSDEs help calculate initial margins in financial contracts.
The paper develops a new model-free formula for option initial margins.
We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat initial data sets either contain such surfaces or are diffeomorphic to R^3. We establish a generalization of the Penrose singularity theorem…
We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This, together with the results in [9], gives a precise sense in which generic initial data c…
Rigidity results for initial data sets related to the positive mass theorem.
Paper proves rigidity of initial data sets with boundary and capillary MOTS.
We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initi…
Study shows how charged MOTS restrict spacetime configurations.
We introduce a dynamic model of the default waterfall of derivatives CCPs and propose a risk sensitive method for sizing the initial margin (IM), and the default fund (DF) and its allocation among clearing members. Using a Markovian structure model of joint credit migrations, our evaluation of DF takes into account the…
New method detects metastable basins in high dimensions using trajectory sampling.
In a recent paper, Eichmair, Galloway and Pollack have proved a Gannon-Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. However, one might wonder whether the corresponding incomplete geodesics could still …
Study shows directional convergence for neural networks under spherical symmetry.
New analysis shows temperature guarantees generalization in stochastic training.
Vacuum gravity shows black holes can form without collapse.
Existence proved for -Bass martingales with specific marginals.
Study learns dynamics of linear systems from multiple short trajectories.
Study on neuron dynamics for XOR classification with zero-margin.
We embed KKT points in neural networks of different sizes.
Margin enlargement over training data has been an important strategy since perceptrons in machine learning for the purpose of boosting the robustness of classifiers toward a good generalization ability. Yet Breiman (1999) showed a dilemma that a uniform improvement on margin distribution does NOT necessarily reduces ge…
Theoretical justification for deep networks' performance with regularization techniques.
In this paper, we investigate risk minimization problem of derivatives based on non-tradable underlyings by means of dynamic g-expectations which are slight different from conditional g-expectations. In this framework, inspired by [1] and [16], we introduce risk indifference price, marginal risk price and derivative he…
Study stability and rigidity of axisymmetric marginally outer trapped surfaces.
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Krühner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point of view. In mathematical t…
Algorithm learns dynamics from past observations.
In a diffusion process on a network, how many nodes are expected to be influenced by a set of initial spreaders? This natural problem, often referred to as influence estimation, boils down to computing the marginal probability that a given node is active at a given time when the process starts from specified initial co…
New method reconstructs non-equilibrium stochastic systems from data.
DGNN predicts financial margin calls under stress tests.
New Langevin dynamics samples from entropy-regularized optimal transport.
In order to protect brokers from customer defaults in a volatile market, an active margin system is proposed for the transactions of margin lending in China. The probability of negative return under the condition that collaterals are liquidated in a falling market is used to measure the risk associated with margin loan…
In this paper we extend the existing literature on xVA along three directions. First, we enhance current BSDE-based xVA frameworks to include initial margin in presence of defaults. Next, we solve the consistency problem that arises when the front-office desk of the bank uses trade-specific discount curves (CSA discoun…
The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach fo…
Gradient descent and SGD achieve low test error in specific network weight regimes.
Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose both theoretical and practical challenges to statistical machine learning algori…
This article prices OTC derivatives with either an exogenously determined initial margin profile or endogenously approximated initial margin. In the former case, margin valuation adjustment (MVA) is defined as the liability-side discounted expected margin profile, while in the latter, an extended partial differential e…
In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of \textsl{possibly non-compact} marginally outer-trapped surfaces (thus extending Hawking's classical theorem on the topology of black holes). We first prove that an unbounded, stable margi…
The paper calibrates geophysical predictions using marginal distributions and machine learning.
Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of boosting algorithms was initiated by Schapire, Freund, Bartlett and Lee (1998) an…