A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Handlebody groups are rigid under measure equivalence.
Investigates set-valued risk measures for processes and vectors, proving equivalence and providing new dual representations.
Study graph products of groups, classifying them up to measure equivalence and rigidity.
Right-angled Artin groups are classified based on measure equivalence.
In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the disc…
The paper develops a new approach to conditional risk measures using modular convex analysis.
The paper studies projections of asset prices under equivalent martingale measures.
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…
New conditional risk measures called conditional generalized quantiles defined and characterized.
All Higman groups on 5 or more generators are uniquely measure equivalent.
Right-angled Artin groups have unique quasi-isometry classes when measure equivalent.
The study examines markets with multiple numéraires and finds equivalent martingale measures.
In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the motivations for this notion. The main result of this paper is ME r…
Paper introduces EEMs for pricing contingent claim returns.
We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping class group is measure equivalent to a discrete group, then they are commensurable up to finite kernel. Moreover, we describe all lattice emb…
The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. The proposed approach accounts for equivalent and non-equivalent p…
New multivariate risk measures improve on univariate OCE methods.
The article provides representations of exchange option prices under SVJD dynamics.
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the numéraire process causes significant chang…
Characterizes measures preserving compound mixed renewal process properties.
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …
Introduces new performance measures using scaled utility functions.
Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.
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…
We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change-point model and we give the conditions for the existence of f-divergence minimal equival…
Study geometrically measures to decide if modular companions are conformally equivalent.
This paper introduces new risk measures for evaluating losses with varying time horizons.
Free group automorphisms group rigidity proven.
We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping cl…
Study tackles causal structure learning in linear models with unobserved variables and measurement error.
Proves is 1-taut, concluding studies of rank-one Lie groups.
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in infinitely many equivalent martingale measures. We find the set equivalent marting…
Submodularity is studied for convex risk measures, including Expected Shortfall.
The main goal of this paper is to define a 1-1 correspondence between between substitution tilings constructed by inflation and the arithmetic of positional representation in the underlying real vector space. It introduces a generalization of inflationary tessellations to equivalence classes of tiles. Two tiles belong …
Researchers prove a new measure for a financial volatility model.
We prove the equivalence of the curvature-dimension bounds of Lott-Sturm-Villani (via entropy and optimal transport) and of Bakry--Émery (via energy and Γ_2$-calculus) in complete generality for infinitesimally Hilbertian metric measure spaces. In particular, we establish the full Bochner inequality on such metric meas…
Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.
Reframed GES uses a neural conditional dependence measure for consistent causal structure learning.
Paper shows equivalence of two curvature notions on singular surfaces.
Artin groups of hyperbolic type are boundary amenable and have rigid properties.
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characteriza…
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of arbitrage and the existence of an equivalent martingale measure is a folk theorem,…
New measure defined for Brakke flow, linking classical and new definitions.
The curvature-dimension condition is a generalization of the Bochner inequality to weighted Riemannian manifolds and general metric measure spaces. It is now known to be equivalent to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein distance contraction properties at different times.…
Proposes a new method to rank risky investments based on Omega measure.
This paper proposes two approaches that quantify the exact relationship among the viability, the absence of arbitrage, and/or the existence of the numéraire portfolio under minimal assumptions and for general continuous-time market models. Precisely, our first and principal contribution proves the equivalence among the…
The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.
An algorithm preserves topological features in dimensionality reduction.