arXiv research

Bayesian method corrects for model selection multiplicity in regression.

A method makes particle filters differentiable without altering their forward pass.

A method uses confidence scores to handle noisy labels for each instance.

Pricing Bermudan swaptions with few exercise dates using analytic methods.

We create precise formulas for VIX option implied volatility.

Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of…

We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We …

Study numerical methods for singular FBSDEs with degenerate forward component.

We revisit the problem of pricing and hedging plain vanilla single-currency interest rate derivatives using multiple distinct yield curves for market coherent estimation of discount factors and forward rates with different underlying rate tenors. Within such double-curve-single-currency framework, adopted by the market…

In this work we derive an approximated no-arbitrage market valuation formula for Constant Maturity Credit Default Swaps (CMCDS). We move from the CDS options market model in Brigo (2004), and derive a formula for CMCDS that is the analogous of the formula for constant maturity swaps in the default free swap market unde…

The paper tackles model misspecification in reinforcement learning through a bootstrapped neural network and error correction.

This study examines deep hedging for S&P 500 options, revealing systematic delta corrections and fragility.

SRFE clarifies KL divergences without unifying learning frameworks.

This paper improves SGMs by using a predictor-corrector scheme to converge faster.

Study shows AD for neural nets with machine-representable numbers can be incorrect.

We consider the mean-variance hedging problem under partial Information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that the initial mean variance hedging problem is equivalent to a ne…

Neural Diffusion Intensity Models simplify Cox processes inference.

We introduce a data-free quantization method for deep neural networks that does not require fine-tuning or hyperparameter selection. It achieves near-original model performance on common computer vision architectures and tasks. 8-bit fixed-point quantization is essential for efficient inference on modern deep learning …

New method verifies formulas for causal interventional distributions.

A new method for math reasoning that allows for iterative correction.

Generative model uses DDPMs for risk-neutral derivative pricing.

We characterize a prevalent weakness of deep neural networks (DNNs)---overthinking---which occurs when a DNN can reach correct predictions before its final layer. Overthinking is computationally wasteful, and it can also be destructive when, by the final layer, a correct prediction changes into a misclassification. Und…

In this paper, the problem of one-bit compressed sensing (OBCS) is formulated as a problem in probably approximately correct (PAC) learning. It is shown that the Vapnik-Chervonenkis (VC-) dimension of the set of half-spaces in $\mathbb{R}^n$ generated by $k$-sparse vectors is bounded below by $k \lg (n/k)$ and above by…

A new training method speeds up ResNet training by 3x with minimal accuracy loss.

VT-DIS improves sampling from Boltzmann distributions with minimal overhead.

U-turn chains improve sampling from complex distributions.

In this paper we push forward results on the invariant ${\cal F}$-module of a virtual knot investigated by the first named author where ${\cal F}$ is the algebra with two invertible generators $A,B$ and one relation $A^{-1}B^{-1}AB-B^{-1}AB= BA^{-1}B^{-1}A-A$. For flat knots and links the two sides of the relation equa…

Transformers without skip connections collapse token representations to a single direction.

Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response to this challenge, there has been considerable recent work based on varying assu…

We quantify forgetting in post-training models, distinguishing mass and drift.

New methods minimize GFlowNet training divergences for better sampling.

SC-Net learns interpretable filters for inverse problems, achieving optimal convergence and super-resolution.

Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs, computes the lower and upper bound on the function values. Because the network and the …

Proposes a new framework for invariant quadratic P&L predictions in option books.

New method for dynamic valuation in markets with random endowments.

We proposed the expected energy-based restricted Boltzmann machine (EE-RBM) as a discriminative RBM method for classification. Two characteristics of the EE-RBM are that the output is unbounded and that the target value of correct classification is set to a value much greater than one. In this study, by adopting featur…

This paper shows how forward rate interpolations are equivalent to discount factor interpolations in yield curve construction.

We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two different parties in the transaction. This formula is only a simplified representati…

Paper explores volatility swaps in rough volatility models.

New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.

Develops a new class of forward performance processes for investment pools.

We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential Lévy models. This expansion applies to both small and large maturities and is based solely on the p…

Bayesian model tackles high-dimensional inverse problems efficiently.

This paper studies robust forward investment and consumption preferences within a zero-volatility context. Different from previous works, we consider an incomplete financial market model due to general investment portfolio constraints. We provide a new PDE characterization and a novel semi-explicit saddle-point constru…

We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure, decorrelation of moves in different points on the forward curve, and implied volatil…

Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener process and a compensated Poisson random measure. A major innovation of the paper is t…

In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a number of properties are proved and discussed. Special attention is given to the c…

The paper analyzes investment and consumption strategies under uncertain market conditions.