We provide a general Doob-Meyer decomposition for -supermartingale systems, which does not require any right-continuity on the system. In particular, it generalizes the Doob-Meyer decomposition of Mertens (1972) for classical supermartingales, as well as Peng's (1999) version for right-continuous -supermartingale…
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48 results for “Azéma supermartingale”
Extended Ville's inequality for nonintegrable supermartingales.
problem Nonintegrable nonnegative supermartingales.
method Derivation of extended Ville's inequality and extension of the method of mixtures.
result Strengthened classical Ville's inequality for nonintegrable settings.
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are characterized as the worst-case dual variables in the dual representation of the risk m…
New inequalities for matrix supermartingales converge under various conditions.
problem Convergence and maximal inequalities of supermartingales in positive semidefinite matrices.
method Developed new concentration inequalities for matrix supermartingales.
result New inequalities for matrix supermartingales under different tail conditions.
Two probability distributions and in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are al…
Sequential tests for nonparametric hypotheses using supermartingales.
problem Designing valid sequential tests for nonparametric null hypotheses.
method Using elicitable and identifiable functionals, nonnegative supermartingales, and Online Convex Optimization.
result Rigorous guarantees on asymptotic power for a wide range of alternative hypotheses.
We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows…
New PAC-Bayes bounds for heavy-tailed losses using supermartingales.
problem Extending PAC-Bayes bounds to heavy-tailed losses.
method Using supermartingales and bounded variance assumption.
result PAC-Bayes generalization bounds for heavy-tailed losses.
Improved bound for Gaussian mechanism in differential privacy.
problem Finding tighter bounds for Gaussian mechanism in differential privacy.
method Presented a new closed form bound for -differential privacy using zero mean Gaussian noise.
result The new bound is always lower and valid for all .
In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it the necessary and sufficient conditions of optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of superm…
Study arbitrage theory without numéraire, generalizing NUPBR.
problem Arbitrage theory in markets without numéraire.
method Disintegration of probability space into crash times.
result Generalization of NUPBR to no unbounded profits with bounded risk.
We present constructions inspired by the Ma-Schlenker example of~\cite{Ma:2012hl} that show the non-rigidity of spherical inversive distance circle packings. In contrast to the use in~\cite{Ma:2012hl} of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary …
In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it an optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of supermartingales relative to a convex set of e…
The Tong-Yang-Ma representations are extended to string links and welded string links.
problem Extending Tong-Yang-Ma representations to string links and welded string links.
method Using the method of Silver and Williams, the authors extend the Tong-Yang-Ma representations.
result The kernels of the extended representations can be described using linking numbers.
Unified proof of knot unknotting bounds using Ma-Qiu index.
problem Finding bounds on the number of moves to unknot knots.
method Using the Ma-Qiu index to bound presentation distances and Gordian distances.
result Unified proof of various unknotting number bounds.
We derive an explicit formula for likelihood function for Gaussian VARMA model conditioned on initial observables where the moving-average (MA) coefficients are scalar. For fixed MA coefficients the likelihood function is optimized in the autoregressive variables 's by a closed form formula generalizing regression c…
New method relaxes PCA orthogonality constraints using explained variance of correlated components.
problem Difficulty in using PCA for sparse design due to orthogonality constraints and non-differentiable penalty.
method Introduce expvar(Y) to measure variance explained by correlated components, relax orthogonality constraints.
result Two expvar(Y) definitions suitable for block PCA formulations without orthogonality constraints.
Given a finite honest time, we first show that the associated Azéma optional supermartingale can be expressed as the drawdown and the relative drawdown of some local optional supermartingales with continuous running supremum. The relative drawdown representation then allows us to provide a characterisation of finite ho…
Study on stability of optimal transport problems for probability measures.
problem Stability of supermartingale optimal transport problems.
method Approximation in adapted Wasserstein distance and continuity of functional.
result Continuity and monotonicity principles for weak supermartingale optimal transport.
New approach for prudent risk evaluation using model aggregation.
problem Risk evaluation and optimization under uncertainty.
method Model Aggregation (MA) approach based on stochastic dominance.
result Produces robust risk evaluation and distributional models.
A Deep Learning Mechanism for Efficient Information Dissemination in Vehicular Floating Contentstat.ML
Handling the tremendous amount of network data, produced by the explosive growth of mobile traffic volume, is becoming of main priority to achieve desired performance targets efficiently. Opportunistic communication such as FloatingContent (FC), can be used to offload part of the cellular traffic volume to vehicular-to…
The paper addresses model averaging and ensembling, providing theoretical and practical insights.
problem Combining least squares estimators from multiple candidate models for improved predictive accuracy.
method Establishes oracle inequalities for Mallows' criterion, proposes a novel Mallows-type MA procedure.
result Demonstrates the effectiveness of the proposed Mallows-type MA estimator through numerical experiments.
A new test detects noise in graph data, useful for forecasting.
problem Detecting uncorrelated noise in graph data.
method Spatio-temporal extension of traditional tests, using graph signals.
result Asymptotic distribution known, no assumption of identically distributed data.
In this paper we construct a Lie algebra representation of the algebraic string bracket on negative cyclic cohomology of an associative algebra with appropriate duality. This is a generalized algebraic version of the main theorem of [AZ] which extends Goldman's results using string topology operations.The main result c…
We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under…
In the context of jump-diffusion market models we construct examples that satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We show that in these examples the only candidate for the density process of an equivalent local martingale measure is a supermartingale that is not a martingale, not even a…
WAVE improves time series forecasting by integrating AR and MA components.
problem Time series forecasting challenges.
method WAVE attention mechanism with AR and MA components.
result WAVE attention consistently improves TSF performance.
Paper proposes MA-BERT for efficient data-driven ATM models.
problem Long training time and need for large datasets in data-driven ATM models.
method Multi-Agent Bidirectional Encoder Representations from Transformers (MA-BERT) and transfer learning framework.
result MA-BERT saves training time and achieves high performance with little data.
We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integ…
In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose where satisfies the restricted isometry property (RIP) with a sufficiently small constant, and . Then minimizing subject to $\Vert y - Az \Ver…
Under short sales prohibitions, no free lunch with vanishing risk (NFLVR-S) is known to be equivalent to the existence of an equivalent supermartingale measure for the price processes (Pulido [22]). For two given price processes, we translate the property (NFLVR-S) in terms of so called structure conditions and we intr…
Proposes a new method for manifold alignment using geometry-regularized twin autoencoders.
problem Traditional MA methods lack out-of-sample extension and real-world applicability.
method Guided representation learning with geometry-regularized twin autoencoders.
result Improves cross-domain generalization and robustness while maintaining alignment fidelity.
Unified framework for anytime-valid PAC-Bayes bounds.
problem Deriving time-uniform PAC-Bayes bounds for stochastic processes.
method Combines four tools: nonnegative supermartingales, method of mixtures, Donsker-Varadhan formula, and Ville's inequality.
result Unified PAC-Bayes theorem for a wide class of discrete stochastic processes.
We solve optimal consumption in a market with bounded risk.
problem Optimal consumption in a semimartingale market with bounded risk.
method Use supermartingale deflators to prove strong duality.
result Strong duality and complete characterisation of optimal consumption.
Study resolves duality gap in optimal consumption with random income termination.
problem Optimal consumption in a market with randomly terminating income.
method Established rigorous duality theory using supermartingale deflators.
result Closed duality gap and characterized optimal wealth process.
Study examines insider trading in short-selling restricted markets.
problem Analyzing insider trading opportunities in short-selling prohibited markets.
method Introducing minimal supermartingale measure and analyzing its properties in relation to minimal martingale measure.
result Conditions under which both measures fail to exist, indicating insider information affecting market perception.
Study asset price bubbles in markets with short sales prohibitions and model uncertainty.
problem Investigating asset price bubbles in markets with short sales prohibitions and model uncertainty.
method Introducing a novel definition of the fundamental price and analyzing the types and characterization of bubbles using a new fundamental theorem of asset pricing and superhedging duality.
result Two distinct types of bubbles arise depending on the maturity structure of the asset, and conditions for their existence are provided.
The Ma-Trudinger-Wang curvature --- or cross-curvature --- is an object arising in the regularity theory of optimal transportation. If the transportation cost is derived from a Hamiltonian action, we show its cross-curvature can be expressed in terms of the associated Jacobi fields. Using this expression, we show the l…
A new method for name disambiguation in academic networks using multi-view attention and recurrent neural networks.
problem Disambiguating authors with the same name in large-scale academic networks.
method Multi-view Attention-based Pairwise Recurrent Neural Network (MA-PairRNN) that divides papers into blocks based on author attributes and merges blocks of the same author.
result MA-PairRNN significantly improves name disambiguation performance on real-world datasets.
Study on positivity properties of vector bundle Monge-Ampère equation.
problem Analyzing positivity in vector bundle Monge-Ampère equation.
method Investigates MA-positivity and MA-semi-positive solutions for different ranks of holomorphic bundles over complex surfaces and manifolds.
result Positivity preservation in rank-two holomorphic bundles but not in higher ranks.
This book, which is in Spanish, provides detailed descriptions, including over 550 mathematical formulas, for over 150 trading strategies across a host of asset classes (and trading styles). This includes stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured asse…
We prove that refined analytic torsion on a manifold with boundary is an analytic section of the determinant line bundle over the representation variety. As a fundamental application we establish a gluing formula for refined analytic torsion on connected components of the complex representation space which contain a un…
Optimal policy for multi-armed multi-action bandits with unknown parameters.
problem Optimal sequential action selection for multi-armed multi-action bandits with unknown parameters.
method Occupancy-Measured-Reward Index Policy (OMRIP) and R(MA)^2B-UCB algorithm.
result Asymptotically optimal policy with sub-linear regret and low computational complexity.
Dynamic risk measuresq-fin.RM
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time consistency properties of dynamic risk measures in terms of acceptance sets, penalty …
Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.
problem Tackles robustness to outliers and adversarial corruptions in mean estimation.
method Designs new robust exponential supermartingales to create confidence sequences.
result Achieves optimal width and shows smaller margin of error compared to fixed-time robust methods.
Several rigidity problems in toric topology are addressed in \cite{ma-su08}. In this paper, we survey results on those problems including recent development.
Agent maximizes utility with pathwise constraint on portfolio value.
problem Maximizing utility with a pathwise constraint on portfolio value.
method Max-plus decomposition for supermartingales, Black-Scholes-Merton model.
result Explicit form of optimal terminal wealth and process involved.