Defines financial models without probability theory.
problem Establishing martingale theory without probability.
method Introducing supermartingales, martingales, and semimartingales in continuous price paths.
result Probability-free versions of martingale results established.
Extends martingale theory to non-monotone information in jump processes.
problem Non-monotone information dynamics in financial and insurance applications.
method Develops a general theory of martingale representations for non-monotone filtrations.
result Introduces a symmetric counterpart to martingale representations that quantifies information loss.
Analyzes robust martingale selection problem and its relation to no-arbitrage theory.
problem Martingale selection problem in a robust setting.
method Derives conditions for solvability and connects to no-arbitrage theory.
result Obtains versions of the Fundamental Theorem of Asset Pricing in various market conditions.
Paper simplifies stock market theory without randomness.
problem Applying stochastic portfolio theory to non-stochastic markets.
method Develops non-stochastic versions of stochastic portfolio theory results.
result Establishes non-stochastic versions of basic stochastic portfolio theory results.
We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to martingales opening the way for…
A concept of martingale-fair index of return, consistent with Arbitrage Free Pricing Theory, is introduced. An explicit formula for the average rate of return of a group of investment/pension funds in a discrete time stochastic model is derived and several properties of this index are shown. In particular, it is proven…
Complete duality theory for martingale optimal transport on the line.
problem Optimal transport between two probability measures on the real line.
method Quasi-sure formulation of the dual problem, showing complete duality theory for general marginals and measurable reward functions.
result Absence of duality gap and existence of dual optimizers for general marginals and measurable reward functions.
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
The paper develops option pricing methods for bilateral Gamma stock models.
problem Developing accurate option pricing measures for bilateral Gamma stock models.
method Incorporates various mathematical techniques including Esscher transforms, minimal entropy martingale measures, and p-optimal martingale measures. result Illustrates the theory with a numerical example, providing practical application of the methods.
Enhances Doob's inequality for sub-martingales.
problem Fundamental importance of Doob's inequality in stochastic process theory.
method Generalization of Doob's Lp inequality for sub-martingales. result A tighter estimate on Doob's inequality for sub-martingales.
Novel proof of Shepp's theorem using martingales.
problem Determining the optimal time to sell a bond.
method Guessing and proving the optimal control function with martingales.
result Proved Shepp's theorem using a novel approach.
We prove that, for locally bounded processes, absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of filtration enlargements.
New method finds closest martingale to Brownian motion.
problem Finding optimal martingale interpolating marginals.
method Martingale Sinkhorn algorithm, iterative scheme.
result Algorithm yields Bass potential in arbitrary dimension.
Solves portfolio selection with constraints using martingale theory.
problem Portfolio selection with constraints on wealth and portfolio.
method Transformed into a mean-variance problem without constraints, solved using martingale theory.
result Directly presents semi-analytical expressions of efficient policy.
The main result of this paper that a martingale evolution can be chosen for Libor such that all the Libor interest rates have a common market measure; the drift is fixed such that each Libor has the martingale property. Libor is described using a field theory model, and a common measure is seen to be emerge naturally f…
New approach shows continuity and compactness of martingale measures.
problem Stability of martingale optimal transport problem.
method Set-valued map theory and lower-upper hemicontinuity.
result Lower and upper hemicontinuity of the set of martingale measures.
Geometric Bass martingales linked to Brownian motion and geometric Brownian motion.
problem Modeling continuous martingales with prescribed initial and terminal distributions.
method Developed geometric Bass martingales and established their properties.
result Explicit bijection and representation of geometric Bass martingales.
Quantum probability theory constructs Martingales for non-Brownian financial models.
problem Constructing Martingales for financial models using fractional Brownian motion.
method Quantum probability theory and Wick product.
result Quantum probability framework allows for Martingale construction without Brownian integrals.
Introduces GIMP processes for multivariate equity derivatives.
problem Evaluating multivariate equity derivatives with martingale pricing.
method Defines GIMP processes with no-Granger-causality of increments in a Markov setting.
result GIMP processes are closed under time change and maintain martingale property.
Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.
problem Entropy Martingale Optimal Transport problem and its associated optimization problem.
method Combines Entropy Optimal Transport and Martingale Optimal Transport theories, with novel penalization terms and constraints.
result Establishes a nonlinear robust pricing-hedging duality, covering various known robust results.
New approach to asset pricing without martingale measures.
problem No-arbitrage condition and martingale measures in financial asset pricing theory.
method Convex duality and Fenchel conjugate for super-replication cost estimation.
result Super-hedging problem leads to a new condition called Absence of Immediate Profit (AIP).
We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical Analysis, 15:89-168, 2009].
Invariance times relate stopping times to martingale properties in probability theory.
problem Characterizing stopping times that preserve martingale properties.
method Analyzing filtrations and stopping times in probability spaces.
result Characterized invariance times in terms of Azéma supermartingales.
Study shows bond market incompleteness with Lévy noise.
problem Incompleteness of forward rate based bond market model driven by Lévy noise.
method Examined the incompleteness of the market when Lévy measure has a density function. Presented theory of stochastic integration and integral representation of local martingales.
result Proven incompleteness of the bond market model under Lévy noise.
Model shows how liquidity drives asset bubbles in financial networks.
problem Understanding how liquidity induces asset bubbles in financial markets.
method Constructive model embedding martingale theory of bubbles.
result Existence of a flow of equivalent martingale measures for market price.
Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from risk-adjusted discounting, we use Perron-Frobenius Theory to isolate a positive martingal…
New probabilistic approach to optimal transport using martingales.
problem Optimal transport between given distributions.
method Martingale formulation of the Benamou-Brenier problem.
result Unique solution mimics Brownian motion and provides time-consistent interpolations.
Entropy-minimal measure calculated for a stochastic volatility model.
problem Calculating the entropy-minimal equivalent martingale measure in a stochastic volatility model.
method Revised related theory, calculated entropy-minimal measure.
result Entropy-minimal measure for the exponential Ornstein-Uhlenbeck model.
New analysis shows LLMs don't follow Bayesian inference in ICL.
problem Does in-context learning in LLMs follow Bayesian inference?
method Analyzes ICL through the martingale property, a requirement for Bayesian inference.
result Violations of the martingale property show LLMs don't follow Bayesian inference.
Novel bounds improve TD learning consistency in RL.
problem Analyzing Temporal Difference learning's performance.
method High-dimensional concentration inequalities and Berry-Esseen bounds for Markov chain induced martingales.
result Sharp high-probability consistency guarantee for TD learning, matching asymptotic variance up to logarithmic factors.
The paper develops a method for self-normalized inference in adaptive experiments.
problem Adaptive experiments require a fixed horizon for ATE estimation, but propensities can change.
method The method uses self-normalized martingale limit theory to estimate ATE.
result The Studentized statistic is asymptotically N(0,1) at the prespecified horizon.
Develops a model for cryptocurrency interest rates.
problem Modeling interest rates for cryptocurrencies.
method Term structure model with zero short rate, price processes of crypto bonds, and expressions for forward rates.
result Model can be calibrated to market data and uses strict local martingales for pricing kernels.
Study derives new equation for reserves in non-monotone information scenarios.
problem Modeling reserves in situations where information is not always increasing.
method Infinitesimal approach to derive generalized stochastic Thiele equation.
result New equation allows for information discarding and solves open problems.
Paper develops MMOT framework for financial applications with neural acceleration.
problem Financial optimization and calibration under multi-period martingale constraints.
method Theoretical analysis, incremental updates, adaptive sparse grids, hybrid neural-projection solver.
result Neural solver achieves 1597x speedup for real-time applications.
This work builds a hedging mechanism for experimental risk.
problem Risk of financial and statistical bankruptcy in experimentation.
method Game-theoretic statistics framework, capitalization of test martingale wealth process, Markowitz portfolio theory, hedging instrument.
result Investigator can hedge against the null hypothesis and avoid ruin.
Researchers develop a new method to value securities with uncertain default or death times.
problem Valuation of securities with uncertain default or death times in markets with additional information.
method Expansion of filtration and martingale representation theorem to handle uncertainty and risk.
result Any martingale in the large filtration stopped at a random time can be decomposed into orthogonal local martingales.
Tutorial on using concentration inequalities for linear system identification.
problem Learning state-space parameters of linear systems.
method Large-deviations and self-normalized martingales.
result Data-dependent and independent bounds on learning rate.
We win EVA2025 by estimating extreme precipitation events using Peaks Over Thresholds and martingale testing.
problem Estimating the probability of extreme precipitation events with limited data.
method Modeling Peaks Over Thresholds with an exponential distribution and using martingale testing for evaluation.
result Our method outperforms other approaches in estimating extreme precipitation events.
Paper proves convergence of SA algorithm via martingale and converse Lyapunov methods.
problem Proves convergence of stochastic approximation algorithm.
method Uses martingale and converse Lyapunov methods to prove convergence.
result Provides alternate proof of convergence for SA algorithm.
The paper factors long-term affine pricing kernels into two components.
problem Understanding long-term behavior of affine pricing kernels.
method Long-term factorization into discounting rate and martingale component.
result Explicit identification of long bond volatility and martingale component volatility.
New algorithm selects robust martingale for optimal stopping problems.
problem Optimal stopping problems in stochastic processes.
method Randomized dual martingale minimization algorithm.
result Efficiently selects Doob martingale as close as possible.
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.
We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes S allowing for a useful integration theory consists precisely of those processes which can be written in the form S=M+A, where M is a local martingale and A is a finite variation proce…
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Paper calculates perpetual put option pricing with drawdown cap.
problem Pricing perpetual American put options with drawdown constraints.
method Derives explicit formula using Black-Scholes model and martingale theory.
result Optimal exercise occurs at first drawdown below a threshold.
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.
An indicator detects short-term asset price bubbles using option quotes.
problem Detecting short-term asset price bubbles in financial markets.
method Martingale theory, SABR model, Bayesian statistical estimation.
result A closed-form martingale defect indicator for detecting asset price bubbles.
New method calibrates local volatility using optimal transport theory.
problem Calibrating local volatility from option prices.
method Formulates a time continuous martingale optimal transport problem to match asset price densities at two dates.
result Reconstructs dynamic of asset price without time interpolation of option prices.