Develops a multivariate aggregation property for unbiased risk premium estimation.
problem Estimating unbiased risk premia from high-frequency returns.
method Introduces a general multivariate aggregation property for multivariate martingales and log martingales.
result Defines realised third and fourth moments for unbiased risk premium measurement.
Study finds optimal martingale coupling between two distributions with minimal entropy.
problem Finding the optimal martingale coupling between two distributions with minimal relative entropy.
method Solving a dual problem to find the log-density of the optimal coupling, which represents the marginal and martingale constraints.
result The log-density of the optimal coupling is given by a triplet of real functions representing the marginal and martingale constraints.
Bayes-assisted confidence sequences improve efficiency for bounded means.
problem Efficient uncertainty quantification for bounded IID means without parametric assumptions.
method Bayesian working predictive model selects adaptive martingale updates maximizing predictive log-growth.
result Asymptotically log-optimal performance with informative priors reducing width and sampling effort.
Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.
problem Implied volatility constraints under finite log-moments.
method Analyzes stock price martingale with finite log-moments, derives new bounds and proof.
result New bounds on implied volatility growth, relaxes moment assumptions.
Investors with high risk aversion always invest during financial bubbles.
problem Optimal investment in a financial bubble model.
method Modeling financial bubbles using strict local martingales and Johansen-Ledoit-Sornette (JLS) model relaxations.
result Investors with high relative risk aversion always invest during financial bubbles.
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.
We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic processes generate uncorrelated, generally nonstationary increments. Generally,…
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.
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.
New bounds on self-normalized martingales improve online linear regression performance.
problem Improving regret bounds in online linear regression.
method Characterizing scale-invariant bounds on self-normalized martingales.
result For d=1, O(logT) doubly-uniform regret is possible; for d>1, sublinear doubly-uniform regret is impossible. Anytime-valid confirmation of label-shift corrections
problem Small-batch scientific deployments with scarce labeled outcomes
method Conditional e-value and martingale-based rule
result Nonnegative martingale and anytime-valid confirmation rule
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.
For any strictly positive martingale S=exp(X) for which X has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log strike. We illustrate the versatility of our expansion by computing t…
Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are initially characterised as solutions to a second-order system of PDEs, then those pay-…
A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.
problem Avoiding moment explosions and preserving stock price martingale property in stochastic volatility models.
method Introduces a one-factor stochastic volatility model with quadratic drift and a linear dispersion function, showing that the quadratic term is crucial.
result The model prevents moment explosions and preserves the martingale property of the stock price process.
We apply a quadratic hedging scheme developed by Foellmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure …
This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: dXt=atdt+σtdWt, where X denotes the log-price and σ is a càdlàg semi-martingale. In the spirit of a series of recent works on the estimation of the cumulated volatility, we here focus …
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from s…
A number of papers claim that a Log Periodic Power Law (LPPL) fitted to financial market bubbles that precede large market falls or 'crashes', contain parameters that are confined within certain ranges. The mechanism that has been claimed as underlying the LPPL, is based on influence percolation and a martingale condit…
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…
Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of the parameters we find a risk-neural measure and provide new formulas for the di…
Improved diffusion models for generative tasks without dimensionality constraints.
problem Sample complexity bounds for learning score functions in diffusion models.
method Dimension-free sample complexity bounds, martingale-based error decomposition, variance reduction technique (Bootstrapped Score Matching).
result Achieved a double exponential improvement in sample complexity over prior results.
Proposes a new log-rank test using RKHSs for robust two-sample analysis.
problem Two-sample problem in right-censored data.
method Test statistic based on supremum of RKHS-weighted log-rank tests.
result Proposed test is omnibus for a specific family of RKHSs.
Formalizes the Fundamental Theorem of Asset Pricing in Lean 4.
problem Formalizing the Fundamental Theorem of Asset Pricing in a proof assistant.
method Formalization in Lean 4 over Mathlib, covering three market settings.
result Constructs the equivalent martingale measure explicitly and proves its properties.
Kernel for Lévy rough paths derived from PDE system.
problem Computing similarity measures for Lévy rough paths.
method Developed a PDE system for the expected signature of inhomogeneous Lévy processes.
result Gaussian martingales' expected signature kernel satisfies a Goursat PDE.
Proves existence of solutions to stochastic heat equations on manifolds.
problem Existence of solutions to stochastic heat equations on Riemannian manifolds.
method Proved existence using Dirichlet forms and Wiener measure.
result Established log-Sobolev inequality for the Dirichlet form in the path space.
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.
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.
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.
This essay quantifies convexities in incomplete markets using entropy, adjusting prices for risk and incompleteness.
problem Quantifying convexities in incomplete markets and adjusting prices for risk and incompleteness.
method Using entropy, the essay quantifies convexities and adjusts prices for risk and incompleteness in incomplete markets.
result A new price principle derived from a log-martingale condition is introduced, matching risk aversion and adjusting for market incompleteness and default risk.
Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.
problem Tackles the martingale Schrödinger bridge in arbitrary dimensions.
method Identifies continuous-time counterpart and relates to variational problems.
result Continuous martingale Schrödinger bridge coincides with Föllmer martingale in irreducible case.
Study shows conditions for local martingales in SDEs with stochastic volatility.
problem Conditions for local martingales in stochastic differential equations with stochastic volatility.
method Examine sufficient conditions for components of SDEs to be strict local martingales or martingales.
result Components of SDEs can be strict local martingales or martingales under certain conditions.
M-FISHER detects and adapts to streaming data shifts with statistical validity and stability.
problem Detecting and adapting to distributional shifts in streaming data.
method Constructs an exponential martingale from non-conformity scores and applies Ville's inequality for detection. Fisher-preconditioned updates for adaptation.
result Establishes M-FISHER as a principled approach for robust, anytime-valid detection and geometrically stable adaptation.
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.
We develop time-uniform confidence spheres for estimating means of random vectors.
problem Sequential mean estimation in high-dimensional spaces.
method Derive time-uniform confidence sphere sequences (CSSs) for various types of random vectors.
result Optimal CSSs for log-concave, sub-Gaussian, and sub-ψ random vectors. Existence proved for q-Bass martingales with specific marginals.
problem Constructing martingales with prescribed marginals close to a reference measure.
method Geometric analysis of parametrized convex polygonal chains.
result Existence and uniqueness of q-Bass martingales with finitely supported initial marginals. The paper proves stability of martingale representations in a broad context.
problem Stability of martingale representations in a general framework.
method Extensive use of martingale theory and convergence properties.
result Each component of the martingale representation converges under Skorokhod topology.
Note on failure of Martingale Wasserstein Inequality in higher dimensions.
problem Analyzing failure of Martingale Wasserstein Inequality in higher dimensions.
method Checking failure in dimension d≥2 and proving a stronger inequality in all dimensions.
result A stronger Maximal Martingale Wasserstein Inequality holds in all dimensions.
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.
Study online linear regression with paid noise reduction.
problem Online linear regression with noisy features and the ability to pay for reduced noise.
method Analyzes regret against optimal predictor, uses matrix martingale concentration.
result Optimal regret rates for known and unknown noise covariance.
This paper introduces an arbitrage-free conic martingale model for credit risk.
problem The lack of an arbitrage-free conic martingale model for credit risk.
method Developed an arbitrage-free conic martingale called Φ-martingale.
result The Φ-martingale model satisfies the immersion property and is suitable for practical applications in credit risk.
Extends optimal transport to dynamic and martingale settings.
problem Dynamic and martingale relaxation of optimal transport problems.
method Extends Benamou-Brenier formula to weak optimal transport and introduces barycentric optimal transport.
result Relates barycentric optimal transport to martingale Benamou-Brenier formula.
Dual martingales improve primal optimal stopping problem efficiency.
problem Optimal stopping problem in the primal formulation.
method Investigation of dual martingales to improve primal methods.
result Accurate dual martingale approximations reduce primal problem variance.
A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via filtration shrinkage, a p…
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.
In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about the martingale property of solution to driftless stochastic differential equations…
Authors prove the existence of a martingale measure in credit risk models.
problem Existence of an equivalent martingale measure in hazard process models of credit risk.
method By identifying a no-arbitrage condition, the authors construct a measure that turns discounted stock and bond prices into martingales.
result The existence of a martingale measure is demonstrated in credit risk models.
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…