Handlebody groups are rigid under measure equivalence.
problem Proving handlebody groups are rigid under measure equivalence.
method Proving superrigidity for measure equivalence of handlebody groups.
result Every countable group measure equivalent to handlebody groups is virtually isomorphic to them.
Investigates set-valued risk measures for processes and vectors, proving equivalence and providing new dual representations.
problem Investigates set-valued risk measures for processes and vectors.
method Utilizes equivalence of risk measures for processes and vectors and their penalty function formulations.
result Provides new dual representation for risk measures for processes in the set-valued framework.
Study graph products of groups, classifying them up to measure equivalence and rigidity.
problem Classifying graph products of groups up to measure equivalence and rigidity.
method Measure-theoretic and structural properties of von Neumann algebras, rigidity theorems.
result Quantified measure equivalence classification and rigidity theorems for graph products.
Right-angled Artin groups are classified based on measure equivalence.
problem Classifying right-angled Artin groups using measure equivalence.
method Proved measure equivalence implies isomorphic extension graphs, and used quasi-isometry results.
result No right-angled Artin group is superrigid for measure equivalence.
The paper studies martingales and super-martingales under a convex set of measures.
problem Understanding martingales and super-martingales in a convex set of equivalent measures.
method Introduced local regular super-martingales and proved necessary and sufficient conditions for their regularity.
result Generalized Doob's decomposition theorem for super-martingales under a convex set of measures.
The paper generalizes Doob's theorem for incomplete markets and defines fair prices.
problem Risk assessment in markets with incomplete information.
method Introducing local regular supermartingales relative to a convex set of equivalent measures and proving the Doob decomposition theorem.
result Generalization of Doob's theorem to incomplete markets and new definition of fair price.
The paper develops a new approach to conditional risk measures using modular convex analysis.
problem Developing a new method for conditional risk measures.
method Random modular approach to conditional certainty equivalents and niveloids in the conditional L∞-space. result Retrieves a conditional variational formula for optimized certainty equivalents and applies it to the conditional entropic risk measure.
The paper studies projections of asset prices under equivalent martingale measures.
problem Understanding the impact of information on asset price bubbles and arbitrage opportunities.
method Analyzes optional projections of local martingales into a smaller filtration under equivalent martingale measures.
result Provides general results and specific examples like inverse Bessel process and stochastic volatility models.
All Higman groups on 5 or more generators are uniquely measure equivalent.
problem Proving uniqueness of measure equivalence for Higman groups.
method Using measured group theory and polyhedral complexes.
result Superrigidity for measure equivalence of Higman groups.
New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
New approach to model risk measurement using Wasserstein distance.
problem Model risk measurement in financial markets.
method Formulates a new theoretical framework based on Wasserstein distance for non-equivalent probability measures.
result Provides practical results that overcome restrictions of previous methods.
Right-angled Artin groups have unique quasi-isometry classes when measure equivalent.
problem Characterizing when right-angled Artin groups are measure equivalent.
method Proving measure equivalence implies quasi-isometry and using geometric properties of cube complexes.
result Measure equivalence of right-angled Artin groups implies quasi-isometry and geometric properties.
The study examines markets with multiple numéraires and finds equivalent martingale measures.
problem Analyzing markets with diverse assets and numéraires.
method Theoretical foundations and results on superreplication prices.
result Existence of equivalent martingale measures in markets with multiple numéraires.
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.
problem Computing expected future prices of contingent claims.
method Dynamic change of measure approach to construct EEMs.
result EEMs provide physical and pricing expectations of contingent claim prices.
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…
New risk measures for multivariate data, consistent and decomposable.
problem Developing consistent risk measures for multiple variables.
method Showed strong consistency leads to decomposition into aggregation and univariate risk.
result Multivariate risk measures are conditional certainty equivalents under strong consistency.
Study shows no equivalent martingale measure in jump-diffusion models.
problem Existence of equivalent martingale measures in jump-diffusion models.
method Constructing examples and analyzing the properties of candidate measures.
result The only candidate for the density process of an equivalent local martingale measure is a supermartingale that is not a martingale.
New multivariate risk measures improve on univariate OCE methods.
problem Improving risk assessment in multivariate settings.
method Inspired by univariate OCE, introduces convex, monotonic, cash-invariant measures.
result Numerical algorithms provide error estimates for computations.
Generalizes Doob's theorem for supermartingales relative to a convex set of measures.
problem Extending Doob's theorem to supermartingales with respect to a convex set of measures.
method Introduced local regular supermartingales and proved an optional Doob decomposition.
result Generalized Doob's theorem to a new class of supermartingales.
New equivalence found between curvature-dimension conditions and Wasserstein distance contraction.
problem Understanding the relationship between curvature-dimension conditions and Wasserstein distance contraction.
method Generalization of curvature-dimension conditions to metric measure spaces and proving equivalence with Wasserstein contraction properties.
result Wasserstein distance contraction properties are equivalent to curvature-dimension conditions.
The article provides representations of exchange option prices under SVJD dynamics.
problem Modeling and pricing exchange options under stochastic volatility and jumps.
method Develops representations for European and American exchange options using SVJD dynamics and equivalent martingale measures.
result Derives integro-partial differential equations and representations for exchange option prices.
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.
problem Preserving compound mixed renewal process properties under different probability measures.
method Characterization of progressively equivalent probability measures.
result Any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures.
Paper proves equivalence between risk measure consistency and supermartingale property.
problem Consistency of multivariate risk measures over time.
method Proves equivalence between time consistency and supermartingale property, characterizes dual variables.
result Characterizes dual variables under which supermartingale is a martingale.
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 …
Optimizing option exercise policies based on variance optimal martingale measure can lead to unappealing results.
problem Optimizing American option exercise policies under the variance optimal martingale measure can result in unappealing policies.
method Optimizing option exercise policies under the variance optimal martingale measure, then anchoring to the resulting value of this policy.
result Optimizing option exercise policies based on the variance optimal martingale measure can lead to unappealing results.
Introduces new performance measures using scaled utility functions.
problem Performance measurement in financial contexts.
method Certainty equivalents defined via scaled utility functions, well-posed portfolio optimization problem under generic conditions.
result Link between portfolio dynamics, benchmark process, and utility function choice in the long-run setting.
Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.
problem Optimizing decision-making under risk in Markov processes.
method Analyzes risk-sensitive criteria using Optimized Certainty Equivalent, including entropic risk and Conditional Value-at-Risk.
result Conditions for the existence of optimal policies and solution procedures are provided.
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.
problem Deciding if two modular companions are conformally equivalent under a given group action.
method Construct a moduli space and equivariant tilings to measure conformal equivalence.
result Presented a geometric measure to decide conformal equivalence of modular companions.
This paper introduces new risk measures for evaluating losses with varying time horizons.
problem Capturing horizon risk and cash non-additivity in risk evaluation.
method Uses BSDEs and shortfall approaches to develop h-generalized shortfall risk measures.
result Introduces hq-entropic risk measures as a new family of fully-dynamic risk measures.
Free group automorphisms group rigidity proven.
problem Proving rigidity of Out(F_N).
method Measure equivalence rigidity, new canonical splittings.
result Superrigidity of Out(F_N).
Study tackles causal structure learning in linear models with unobserved variables and measurement error.
problem Challenges of unobserved common causes and measurement error in causal structure learning.
method Introduces LV-SEM-ME model with four types of variables and characterizes identifiability under separability condition.
result Establishes form of identification robustness for target effect in broader LV-SEM-ME model.
Proves PU(n,1) is 1-taut, concluding studies of rank-one Lie groups.
problem Tautness of rank-one Lie groups of non-compact type.
method Proves PU(n,1) is 1-taut. result Concludes the study of 1-tautness of rank-one Lie groups of non-compact type. 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…
Submodularity is studied for convex risk measures, including Expected Shortfall.
problem Characterizing submodularity in convex risk measures.
method Analyzing submodularity properties of law-invariant coherent risk measures, including Expected Shortfall and Value-at-Risk.
result AES is submodular only when it reduces to ES, and empirical analysis shows AES violations are less frequent than VaR and ES violations.
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…
Researchers prove a new measure for a financial volatility model.
problem Modeling financial volatility with a Hawkes process.
method Prove existence of equivalent martingale measures for a Heston-Hawkes model.
result Existence of a family of equivalent martingale measures for the 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.
problem Computing divergence between Gaussian measures in infinite-dimensional Hilbert space.
method Closed form expression and regularization for divergence calculation.
result Closed form expression and regularization for Geometric Jensen-Shannon divergence.
Reframed GES uses a neural conditional dependence measure for consistent causal structure learning.
problem Identifying causal structure in nonparametric settings.
method Reframed GES algorithm with a neural conditional dependence measure.
result Optimality and consistency of the reframed GES algorithm under standard assumptions.
Paper shows equivalence of two curvature notions on singular surfaces.
problem Equivalence of two curvature notions on singular surfaces.
method Demonstrates equivalence between two curvature definitions.
result Inequalities of curvature measure imply Alexandrov curvature bounds.
Artin groups of hyperbolic type are boundary amenable and have rigid properties.
problem Characterizing rigidity and measure equivalence properties of Artin groups.
method Analyzing boundary amenability, measure equivalence, and fixed set graphs.
result Measure equivalent Artin groups of hyperbolic type have isomorphic fixed set graphs.
Paper defines tiling correspondence via positional representation.
problem Defining 1-1 correspondence between tilings and positional representation.
method Generalizes inflationary tessellations to equivalence classes of tiles.
result Multiplier of inflation tilings is an algebraic number.
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.
problem Defining and characterizing the Brakke flow.
method Introduced a space-time-Grassmann measure to characterize the flow.
result Equivalence between classical and new definitions of the Brakke flow.