Paper tackles non-convex optimization for higher moments in portfolio management.
problem Complexity of higher moments in optimization problems.
method Method of successive convex approximation.
result Solves mean-variance-skewness problem using non-convex optimization.
In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension namely, HAdam, which uses higher order moments of the stochastic gradient. Our …
Improved GAN performance using higher-order Wasserstein moments.
problem Stabilizing and enhancing GANs for better mode coverage and stability.
method Deriving and training a GAN with a modified Wasserstein distance using higher-order moments.
result Training a GAN with higher-order Wasserstein moments improves performance, even with increased computational cost.
The paper classifies various higher moments portfolio optimization methods.
problem Optimizing portfolios with higher moments like skewness and kurtosis.
method Review of different optimization paradigms including utility and multi-objective approaches.
result Comparison of advantages and disadvantages of various methods.
The paper examines higher moments in insurance, focusing on coskewness and its impact on actuarial quantities.
problem The impact of higher-order moments on actuarial applications, particularly expected shortfall and life annuity valuation.
method Derives analytical bounds for mixed moments under unspecified dependence structure, applies copula-based mixture model.
result Coskewness and odd-order mixed moments exhibit a monotonic relationship with expected shortfall and annuity premiums.
Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.
problem Time-inconsistent stochastic control problems with mean and higher-order moments.
method Developed closed-loop and open-loop Nash equilibrium controls using PDEs and maximum principles.
result Identical closed-loop and open-loop Nash equilibria controls, independent of state value and random path.
The paper introduces moment multicalibration for estimating uncertainty across subgroups.
problem Ensuring fairness and accurate uncertainty estimation in predictions across different subgroups.
method Develops a method for multicalibration of higher moments, enabling point predictions and interval estimation.
result Moment multicalibration allows for valid prediction intervals that are fair across various subgroups.
Study shows different types of volatility and skewness changes affect stock prices.
problem Different types of volatility and skewness changes affect stock prices.
method Used intraday data for individual stocks to analyze cross-section of asset returns.
result Idiosyncratic transitory and persistent shocks to volatility and skewness are priced differently in stock returns.
Moment Pooling reduces latent space dimensions in machine learning models.
problem High-dimensional latent spaces in machine learning models are hard to interpret.
method Moment Pooling extends Deep Sets networks to arbitrary multivariate moments.
result Latent dimensions as small as 1 can achieve similar performance to higher dimensions.
We derive a general multivariate theory for realised characteristics of `model-free discretisation-invariant swaps', so-called because the standard no-arbitrage assumption of martingale forward prices is sufficient to derive fair-value swap rates for such characteristics which have no jump or discretisation errors. Thi…
Paper provides Edgeworth expansions for network moments, improving accuracy of sampling distributions.
problem Accurate descriptions of sampling distributions of network moment statistics.
method Edgeworth expansion applied to studentized network moment statistics.
result Higher-order accurate approximation to sampling CDF of network moment statistics.
We develop a general multivariate aggregation property which encompasses the distinct versions of the property that were introduced by Neuberger [2012] and Bondarenko [2014] independently. This way, we classify new types of model-free realised characteristics for which risk premia may be estimated without bias. We focu…
Paper characterizes equilibrium strategies for stochastic control with higher-order moments.
problem Stochastic control problems with higher-order moments.
method Novel characterization of time-consistent control problems, deriving equilibrium conditions via BSDEs.
result Derives sufficient and necessary conditions for an open-loop Nash equilibrium control (ONEC) in a novel way.
New invariants detect Fano varieties' K-stability.
problem Detecting K-stability in Fano varieties.
method Introducing valuative invariants based on higher moments.
result Can detect K-stability of Fano varieties.
Sharp inequalities in unit ball with constraints on moments.
problem Establishing Sobolev trace inequalities with constraints.
method Constructing smooth test functions for higher order moments.
result Almost optimal Sobolev trace inequalities for 2nd and 4th orders.
Algorithm tackles large-scale portfolio optimization with higher moments, improving computational efficiency.
problem Optimizing portfolios with higher moments (variance, skewness, kurtosis) for large asset universes is computationally infeasible.
method Developed a structure-exploiting algorithm based on Yau's affine-normal descent, working directly with return matrix.
result Algorithm avoids explicit higher-order tensors and exploits quartic structure for efficient computation.
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order and replacing higher order terms with functions of lower order ones. For a give…
Moment polytope of toric exponential families is a projection of a simplex.
problem Understanding the geometry of exponential families in finite sample spaces.
method Toric torification and projection of higher-dimensional simplices.
result Moment polytope is a projection of a higher-dimensional simplex.
Betas are possibly the most frequently applied tool to analyze how securities relate to the market. While in very widespread use, betas only express dynamics derived from second moment statistics. Financial returns data often deviate from normal assumptions in the sense that they have significant third and fourth order…
Paper proposes an efficient algorithm to handle high-order portfolio moments.
problem Designing portfolios with high-order moments (skewness and kurtosis) is computationally challenging.
method Proposes a SCA algorithm framework for solving high-order portfolios efficiently.
result Demonstrates the efficiency of the proposed algorithm through numerical experiments.
New proof of Sobolev inequality with constraints on sphere.
problem Improving Sobolev inequality on sphere with constraints.
method Careful study of extremal problem on sphere.
result Explicit determination of constant in second order moments case.
Approximates discounted moments for financial products using polynomial expansions.
problem Approximating discounted moments of stochastic processes for financial applications.
method High-order power series expansion of the infinitesimal generator.
result Error decreases to around 10 to 100 times machine precision for higher orders.
New rigidity results for complex and quaternionic moment-angle manifolds.
problem Equivariant topological rigidity of complex and quaternionic moment-angle manifolds.
method Reduction to equivariant rigidity of quasitoric (or quoric) quotients and principal bundles.
result Full equivariant rigidity for manifolds with four-dimensional quoric quotients and primary rigidity for higher dimensions.
We compute higher moments of the Siegel--Veech transform over quotients of SL(2,R) by the Hecke triangle groups. After fixing a normalization of the Haar measure on SL(2,R) we use geometric results and linear algebra to create explicit integration formulas which give information about densities of…
We propose a method of moments (MoM) algorithm for training large-scale implicit generative models. Moment estimation in this setting encounters two problems: it is often difficult to define the millions of moments needed to learn the model parameters, and it is hard to determine which properties are useful when specif…
The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature representations directly in the hidden activation space. Although some standard distributi…
Proposes DWMD for better matching of hidden representations across domains.
problem Measuring data distribution discrepancy between semantically related domains for feature representation matching.
method DWMD, a moment-based probability distribution metric that explicitly orders and weights higher-order moments.
result DWMD is error-free and can strictly reflect distribution differences without feature distribution assumptions.
New method quantifies uncertainty in denoising models.
problem Uncertainty quantification in denoising models.
method Derives a relation between posterior moments and derivatives, uses it for efficient uncertainty quantification.
result Efficient computation of principal components and full marginal distributions of the posterior.
Introduces derived Lie n-groupoids with shifted symplectic structures.
problem Defines structures for higher groupoids and their symplectic properties.
method Introduced derived Lie n-groupoids and their shifted symplectic structures, defining shifted lagrangian structures and proving composition well-defined.
result Shows that the framework includes various reduction procedures.
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent α having its own distribution. We show the effect of stochasticity of α on the expectation and higher moments of the random variable. For instance, the moments of a right-tailed or right-asymmetric varia…
Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.
problem Slower convergence of ICA in high-dimensional data with high-order moments.
method High-dimensional ODE analysis of ICA algorithm under controlled moment structure.
result Critical learning rate threshold for effective ICA when moments are high.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
problem Capturing higher-order tail behavior and dependence effects in risk measures.
method Second-order asymptotic expansions using extreme value theory and regular variation theory.
result Second-order approximations reduce approximation errors, especially at extreme confidence levels.
Optimizes mixture models without parametrizing distributions using tensor decomposition.
problem Estimating conditionally-independent mixture models in high dimensions.
method Alternating least squares optimization scheme for tensor decomposition.
result Competitive performance and applicability to various models and applications.
The paper improves CR Sobolev inequalities and classifies minimizers.
problem Higher-order CR Sobolev inequalities on the CR sphere.
method Improvement through vanishing higher order moments of the volume element.
result New direct proof of minimizers' classification and existence of minimizers in C2k(N). We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to model two-alternative forced choice decisions, and, while simple formulae for ac…
Realized moments of higher order computed from intraday returns are introduced in recent years. The literature indicates that realized skewness is an important factor in explaining future asset returns. However, the literature mainly focuses on the whole market and on the monthly or weekly scale. In this paper, we cond…
The paper explores how market-based returns depend on past trade values.
problem Improving accuracy in forecasting market-based average and volatility of returns.
method Derives the dependence of market-based volatility and higher statistical moments of returns on statistical moments and correlations of current and past trade values.
result Market-based statistical moments can be approximated by a finite number of moments, improving forecast reliability.
Spectral learning extends matrix methods to tensors for better latent variable modeling.
problem Limitations of matrix-based spectral methods in capturing non-Gaussian data.
method Extend spectral decomposition to tensor-based methods for higher-order moments.
result Tensor decomposition can identify latent effects missed by matrix methods.
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…
Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group actions on these manifolds, we introduce a theory of homotopy moment maps. Such a…
Study on martingale property and moment explosions in signature volatility models.
problem Analyzing the martingale property and moment explosions in signature volatility models.
method Fine analysis of the explosion time of a signature stochastic differential equation.
result The price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative.
A classical result of Aubin states that the constant in Moser-Trudinger-Onofri inequality on S2 can be imporved for furnctions with zero first order moments of the area element. We generalize it to higher order moments case. These new inequalities bear similarity to a sequence of Lebedev-Milin type inequa…
Framework predicts nonlinear system responses using GFDT and generative models.
problem Predicting higher-order moments of nonlinear stochastic systems to small perturbations.
method Combining GFDT with generative modeling to estimate score function directly from data.
result Accurately captures nonlinear and non-Gaussian features of system responses.
We use the P&L on a particular class of swaps, representing variance and higher moments for log returns, as estimators in our empirical study on the S&P500 that investigates the factors determining variance and higher-moment risk premia. This class is the discretisation invariant sub-class of swaps with Neuberger's agg…
We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of our present work is dependent on the so-called renewal-reward theorem. Assuming th…
Novel neural network predicts electricity prices with higher moments.
problem Probabilistic forecasting of volatile electricity prices.
method Distributional neural network with a probability layer.
result Significantly outperforms benchmarks in forecasting.
DGMM improves Gaussian mixture modeling efficiency and stability.
problem Efficiently estimating Gaussian mixtures in high dimensions.
method Diagonally-weighted generalized method of moments (DGMM).
result DGMM achieves smaller estimation errors with shorter runtime.
For a finite-dimensional (but possibly noncompact) symplectic manifold with a compact group acting with a proper moment map, we show that the square of the moment map is an equivariantly perfect Morse function in the sense of Kirwan, and that the set of critical points of the square of the moment map is a countable dis…