arXiv research

We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly …

Bayesian neural networks can be partially stochastic without losing predictive power.

Clarifies when solutions to stochastic PDEs stay near given subsets.

New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.

This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the one generated by the asset prices, and the unobservable processes will be modeled …

Paper tackles active labeling for partial supervision.

Improves model accuracy for neural nets in stochastic dynamics with partial prior knowledge.

Neural networks solve SPDEs using Wiener chaos expansion.

IDS optimizes regret in stochastic partial monitoring with linear rewards.

This work explains GANs as Bayesian neural networks with partial stochasticity.

The goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by Lévy processes admits an affine realization. Our results are accompanied by several examples arising in natural sciences and economics.

SON learns SPDE solutions and uncertainty from noisy data.

Solves optimal control for stochastic processes with absorbing states.

The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.

Novel framework for learning infinitesimal generator of stochastic processes.

New approach handles stochastic and partially-observable environments using discrete autoencoders and Monte Carlo tree search.

We establish a stochastic maximum principle (SMP) for control problems of partially observed diffusions of mean-field type with risk-sensitive performance functionals.

Deep learning scheme identifies and reconstructs chaotic and stochastic systems from noisy data.

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equat…

Paper develops efficient Bayesian inference for enzymatic SRNs with LNA metamodel.

Most of the empirical studies on stochastic volatility dynamics favor the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model is reported to be able to capture the volatility skew evolution better than the Heston model. In this …

New model captures state-dependent variability in partially observed systems.

Computational aspects of the optimal consumption and investment with the partially observed stochastic volatility of the asset prices are considered. The new quantization approach to filtering - density quantization - is introduced which reduces the original infinite dimensional state space of the problem to the finite…

Novel framework discovers SPDEs from limited data.

New framework for ranking distributions using variable fractional parameters.

New algorithms reduce regret in both stochastic and adversarial partial monitoring problems.

A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture parsimoniously key stylized facts of the entire implied volatility surface, including extr…

Deep learning model solves high-dimensional PDEs using Actor-Critic approach.

A new method speeds up option pricing under Heston's stochastic volatility model.

Deep learning approximates SPDE solutions from noise trajectories.

PLoM learns stochastic solutions to PDEs with limited data.

Model optimizes trading strategy with unobservable toxicity.

New method improves training stochastic neural networks with tighter guarantees.

TOFU-POV tackles partially observed linear bandits, achieving sublinear regret with low-dimensional action vectors.

Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for solving forward and inverse problems associated with partial differential equati…

Unified framework models multiple financial and insurance term structures.

New method achieves optimal performance without needing problem parameters.

This paper constructs Brownian motion on complex flag manifolds and finds joint distribution of stochastic areas.

Improved Bayesian neural network inference by selectively removing redundant modes.

We construct normed spaces of real-valued functions with controlled growth on possibly infinite-dimensional state spaces such that semigroups of positive, bounded operators $(P_t)_{t\ge 0}$ thereon with $\lim_{t\to 0+}P_t f(x)=f(x)$ are in fact strongly continuous. This result applies to prove optimal rates of converge…

Paper introduces efficient methods for estimating cross-partial derivatives and sensitivity indices.

A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster ass…

This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a bond. In the considered model firstly proposed by [3], the mean returns of individu…

Study on hedging and valuation of basis risk in incomplete markets with partial information.

Derives Black-Scholes model without stochastic calculus or PDEs.

Investigates optimal PPI strategies to reduce carbon emissions while managing financial risk.

We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or permuted during the protocol. In this work, we propose a framework that treats the un…

These notes were originally written for the Stochastic Analysis Seminar in the Department of Operations Research and Financial Engineering at Princeton University, in February of 2011. The seminar was attended and supported by members of the Research Training Group, with the author being partially supported by NSF gran…