arXiv research

The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.

The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are…

The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. \cite{AIS}, and Arai …

We explore a new method for discrete-time control problems using randomization and entropy.

Paper learns DAGs with quadratic variance functions efficiently.

Model asset pricing with habit formation in a large market.

The paper solves a utility-based hedging problem with quadratic costs.

We investigate a class of quadratic-exponential growth BSDEs with jumps. The quadratic structure introduced by Barrieu & El Karoui (2013) yields the universal bounds on the possible solutions. With local Lipschitz continuity and the so-called A_gamma-condition for the comparison principle to hold, we prove the existenc…

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in thei…

Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.

Investor optimizes investment timing with future knowledge, overcoming transaction costs.

A new method for exponentially weighted moving models using approximations.

In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete equilibrium is characterized by a …

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory…

We examine optimal quadratic hedging of barrier options in a discretely sampled exponential Lévy model that has been realistically calibrated to reflect the leptokurtic nature of equity returns. Our main finding is that the impact of hedging errors on prices is several times higher than the impact of other pricing bias…

Develops asset pricing models with mean field game theory for heterogeneous agents.

New theory extends LQ control to non-exponential discount scenarios.

On a complete non-compact gradient shrinking Ricci soliton, we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable. This growth condition is sharp. As an application, we give a necessary and sufficient condition on the solvability of the backwa…

Accelerated gradient method's stability deteriorates exponentially with steps.

Bayesian approach generalizes ADMM for federated learning.

Deep-HGP uses Bayesian nonparametric approach for complex data regression.

Gaussian equivalence fails for simple polynomial embeddings in quadratic scaling RF models.

New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.

This paper develops sparse alternatives to continuous distributions, including new types of Gaussians and attention mechanisms.

New method for Bayesian inference of Lévy-driven SDEs with jumps.

We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan's (1995) delta hedge. Since the minimal m…

Stochastic mirror descent (SMD) is a fairly new family of algorithms that has recently found a wide range of applications in optimization, machine learning, and control. It can be considered a generalization of the classical stochastic gradient algorithm (SGD), where instead of updating the weight vector along the nega…

A novel approach termed \emph{stochastic truncated amplitude flow} (STAF) is developed to reconstruct an unknown $n$-dimensional real-/complex-valued signal $\bm{x}$ from $m$ `phaseless' quadratic equations of the form $ψ_i=|\langle\bm{a}_i,\bm{x}\rangle|$. This problem, also known as phase retrieval from magnitude-onl…

We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior turns out to depend on the correlation between the components, and the explicit s…

Proves new concentration inequalities for sub-gaussian and sub-exponential variables.

The paper rethinks the use of exponential averaging in machine learning optimization.

Quantum UCB algorithm reduces reinforcement learning regret exponentially.

Classifies surfaces in hyperbolic space with constant Gaussian curvature.

Revisits stochastic collocation with exponential splines for option pricing.

RL solves discrete LQ control with Gaussian optimal policy.

Unified analysis of Gaussian Process Thompson Sampling without discretization.

LqgOpt learns optimal control in unknown LQG systems with minimal regret.

New approach to portfolio optimization shows entropy regularization is ineffective.

Bayesian Markowitz portfolio problem shows entropy regularization is ineffective.

We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and linear inverse problems via penalization, and we do not exclude that its scope of a…

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and quadratic loss, SVM with Gaussian kernel can reach the almost optimal learning rate, p…

Unified approach to stability conditions on surfaces with quadratic differentials.

Efficient method for learning continuous exponential families beyond Gaussian.

In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is …

Choquet regularization improves exploration in RL.

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple $(Y,Z,ψ)$ where $Y$ is a semimartingale, and $(Z,ψ)$ are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of …

Faster algorithms for structured SVMs reduce computation time.

Let $g \colon S \looparrowright N$ be a properly immersed $π_1$--injective surface in a non-geometric $3$--manifold $N$. We compute the distortion of $π_1(S)$ in $π_1(N)$ and show that how it is related to separability of $π_1(S)$ in $π_1(N)$. The only possibility of the distortion is linear, quadratic, exponential, an…