arXiv research

The paper derives formulas for moments of a Student t distribution and applies them to quantify $L_p$-quantiles.

New algorithm for risk-sensitive reinforcement learning with natural policy gradients.

This paper examines how data affects risk measures in uncertain distributions.

Stiefel-Whitney classes of moment-angle manifolds are trivial.

The paper derives risk measures for metalog distributions.

The paper analyzes extreme risk measures with limited distributional information.

The third moment variation of a financial asset return process is defined by the quadratic covariation between the return and square return processes. The skew and fat tail risk of an underlying asset can be hedged using a third moment variation swap under which a predetermined fixed leg and the floating leg of the rea…

Given a multisymplectic manifold $(M,ω)$ and a Lie algebra $\frak{g}$ acting on it by infinitesimal symmetries, Fregier-Rogers-Zambon define a homotopy (co-)moment as an $L_{\infty}$-algebra-homomorphism from $\frak{g}$ to the observable algebra $L(M,ω)$ associated to $(M,ω)$, in analogy with and generalizing the notio…

Python package ajdmom simplifies moment formula derivation for jump diffusions.

MuML models predict molecular dipole moments using atomic partial charges and dipoles.

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this work, we consider the case in which certain dimensions of the data are not always …

Many interesting real world domains involve reinforcement learning (RL) in partially observable environments. Efficient learning in such domains is important, but existing sample complexity bounds for partially observable RL are at least exponential in the episode length. We give, to our knowledge, the first partially …

Paper develops methods for inference on time series data using neural networks and sieves.

This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample s…

New method learns near-optimal policies with polynomial samples in A and H.

We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not locally convex near the singularity corresponding to the ring singularity in the…

Generalizes moment-angle manifolds to arbitrary nice manifolds with corners.

Study compares Kähler quotients of torus actions under varying moment maps.

Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.

Paper proposes robust risk measures for non-negative risks with partial information.

A new method extracts features and reconstructs moments in dynamical systems using information geometry.

Paper derives analytical formulas for NLD-CEV moments with regime switching.

We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic-demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving an…

New estimator learns symmetric dynamics from few observations.

Study of generalized almost-Kähler-Ricci solitons and their implications.

Let $P$ be a simple polytope of dimension $n$ with $m$ facets and $P_{v}$ be a polytope obtained from $P$ by cutting off one vertex $v$. Let $Z=Z(P)$ and $Z_{v}=Z(P_{v})$ be the corresponding moment-angle manifolds. In \cite{[GL]} S.Gitler and S.López conjectured that: $Z_{v}$ is diffeomorphic to $\partial[(Z-int(D^{n+…

We study the J-flow on the toric manifolds, through study the transition map between the moment maps induced by two Kähler metrics, which is a diffeomorphism between polytopes. This is similar to the work of Fang-Lai, under the assumption of Calabi symmetry, they study the monotone map between two intervals. We get a p…

A new game-theoretic approach balances downside risk with expected reward.

As a generalization of Kahler-Einstein metrics for Fano manifolds with nonvanishing Futaki invariant, Mabuchi solitons are critical points of a Calabi-type energy functional. We study their existence on toric Fano varieties and the underlying algebraic stability notion: relative Ding stability. As a toy model for a YTD…

We introduce $Z$-critical connections for holomorphic vector bundles and prove their existence under stability conditions.

We show under weak hypotheses that $\partial X$, the Roller boundary of a finite dimensional CAT(0) cube complex $X$ is the Furstenberg-Poisson boundary of a sufficiently nice random walk on an acting group $Γ$. In particular, we show that if $Γ$ admits a nonelementary proper action on $X$, and $μ$ is a generating prob…

We adapt to an infinite dimensional ambient space E.R. Reifenberg's epiperimetric inequality and a quantitative version of D. Preiss' second moments computations to establish that the set of regular points of an almost mass minimizing rectifiable $G$ chain in $\ell_2$ is dense in its support, whenever the group $G$ of …

We prove that the Halperin-Carlsson conjecture holds for any free (Z_2)^m action on a compact manifold whose orbit space is a small cover. In addition, we show that if the total space of a principal (Z_2)^m bundle over a small cover is connected, it must be equivalent to a partial quotient of the corresponding real mom…

Method estimates posterior model for boundary value problems with uncertain constraints.

Study minimal Lagrangian tori on Kähler manifolds, answering questions about their existence and stability.

This paper analyzes MaskGIT sampler and introduces a moment sampler for faster masked diffusion sampling.

New method for inference on strongly identified functionals even when nuisance functions are weakly identified.

Double machine learning provides $\sqrt{n}$-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an $n^{-1/4}$ rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance param…

Paper proposes a policy gradient method for confounded POMDPs.

Consider a random vector with finite second moments. If its precision matrix is an M-matrix, then all partial correlations are non-negative. If that random vector is additionally Gaussian, the corresponding Markov random field (GMRF) is called attractive. We study estimation of M-matrices taking the role of inverse sec…

For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random variables in the combination. It turns out that under suitable conditions on the join…

This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterised by the free boundary problem of a fractional partial differential equation (FPDE) system. Using the technique of approximation we prove t…

Paper finds robust $Λ$-quantiles equal to extremal distributions.

Study of dHYM connections on ruled surfaces with variable background metrics.

The trade of a fixed stock can be regarded as the basic process that measures its momentary price. The stock price is exactly known only at the time of sale when the stock is between traders, that is, only in the case when the owner is unknown. We show that the stock price can be better described by a function indicati…

The paper proposes a method to monitor deep learning predictions for retraining, reducing costs.

In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous mode…

DPFRL uses particle filters for decision making with complex visual observations.