arXiv research

New model for Knightian uncertainty with jumps.

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.

Unified theory of $θ$-expectations derived from chaotic dynamics.

Develops non-linear affine processes for modeling interest rates under parameter uncertainty.

This paper compares expected and distributional reinforcement learning methods.

Optimizes non-linear outcomes from summed contributions.

The study models market price movement based on investors' expectations.

Quantum computing offers a quadratic speedup for estimating non-linear functionals.

Optimal stopping problem solved for irregular reward processes without regularity assumptions.

New algorithm approximates conditional expectations with fast convergence.

Study finds sales forecasters overreact to extreme news.

In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of the…

C-ADAM is a new adaptive solver for complex nested problems.

This essay quantifies convexities in incomplete markets using entropy, adjusting prices for risk and incompleteness.

In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an a…

In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver $g$ is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of $g$-Snell enveloppe. Then, in a second step, we re…

Noise improves model quality in non-linear neural networks during decentralized training.

CRCCA framework improves non-linear CCA with compressed representations.

The paper analyzes portfolio selection with non-linear wealth dynamics and random coefficients.

Paper proposes using expectation models for planning in stochastic environments.

New algorithm tames non-linear growth in stochastic optimization.

The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power…

Study contextual bandits with stage-wise constraints, proving regret bounds and extending results.

New model explains market dynamics with phase transitions and non-linear interactions.

Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party's wealth, whereas both parties must sign for such contracts to exist. Classically, the puzzle is resolved by introducing non-linear utility functions, which encode asymmetric risk preferences; or by assuming the p…

Improved bounds for non-linear SA with fast convergence.

Improved regret bound for multinomial logistic bandits with non-linearity.

This paper studies risk-averse online learning, showing differences from risk-neutral approaches.

Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.

We derive asset pricing formula for markets with incomplete information and subjective views.

Introduces Neural-Brownian Motion for modeling dynamics under learned uncertainty.

Paper introduces a new algorithmic framework for model-based RL with theoretical guarantees.

Paper presents a deep learning method for estimating asset return precision matrices in noisy financial markets.

Study optimal stopping and a non-zero-sum game with risk measures in discrete time.

It is well-known from the work of Schönbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The Stochastic Local Intensity (SLI) models such as the one proposed by Arnsdorf and Halperin…

Bayesian optimization selects experiments for causal structure learning in Gaussian process networks.

The study explores how machine learning can enhance scientific research.

We develop an option pricing model based on a tug-of-war game. This two-player zero-sum stochastic differential game is formulated in the context of a multi-dimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. W…

We study a multiplicative transient price impact model for an illiquid financial market, where trading causes price impact which is multiplicative in relation to the current price, transient over time with finite rate of resilience, and non-linear in the order size. We construct explicit solutions for the optimal contr…

This research uses DPPs to improve semi-parametric regression models.

Despite the fact that the Euler allocation principle has been adopted by many financial institutions for their internal capital allocation process, a comprehensive description of Euler allocation seems still to be missing. We try to fill this gap by presenting the theoretical background as well as practical aspects. In…

DDR estimates personalized treatment effects from clinical trials.

We introduce a new, efficient, principled and backpropagation-compatible algorithm for learning a probability distribution on the weights of a neural network, called Bayes by Backprop. It regularises the weights by minimising a compression cost, known as the variational free energy or the expected lower bound on the ma…

Bayesian approach models match and non-match score distributions over continuous covariates.

MOVDA improves skill ratings by considering margin of victory deviations.

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the componen…

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models and as such are arguably more flexible, have a greater capacity to generalise, …

In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes of Nash equilibria. We then extend this work through a substan…