Stability proved for martingale and weak transport problems.
problem Stability of martingale and weak optimal transport problems.
method Established stability through unconventional topology considering temporal structure of martingales.
result Proved stability of martingale and weak transport problems.
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.
We extend martingale transport results to weak martingale transport.
problem Applying martingale transport results to weak martingale transport.
method Change of numeraire for weak martingale transport.
result Established the correspondence between stretched Brownian motion and its geometric counterpart.
Optimal martingale transport plans without structural assumptions.
problem Finding optimal martingale transport plans.
method Left-monotone martingale coupling and Skorokhod embedding.
result Left-monotone coupling is optimal under specific conditions.
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.
New computational methods solve martingale optimal transport problems.
problem Solving martingale optimal transport problems with additional dynamics constraints.
method Discretization of marginal distributions combined with linear programming and entropic regularisation.
result Approximation of the MOT value using linear programming problems.
Dynamic reinsurance aims to minimize surplus risk using martingale transport.
problem Minimizing surplus risk in dynamic reinsurance.
method Martingale optimal transport techniques.
result A tractable solution analogous to the Bass martingale is found.
The paper solves optimal transport problems with domain constraints.
problem Optimal transport problems with domain constraints.
method Characterizes existence of a probability measure with convex transport constraints.
result Obtains Kantorovich duality and monotonicity principle.
The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the…
Efficiently computes robust option prices using multi-marginal martingale transport.
problem Computing robust option prices under martingale constraints.
method Extending state space, sequential martingale structure, entropic regularisation.
result Fast computation of optimal solutions for large problems.
Paper solves optimal transport with neural nets, also detects anomalies.
problem Optimal transport problems with twist conditions.
method Primal-dual algorithm for neural networks.
result Solves financial data generation and anomaly detection.
Paper uses neural networks to solve complex transport problems.
problem Optimal transport and related hedging problems.
method Penalization and neural networks to solve optimization problems.
result Effective solution to multi-marginal, martingale optimal transport problems.
Extends martingale transport for robust finance problems.
problem Addressing specific robust finance problems not covered by standard martingale transport.
method Introduces an additional parameter to the weak martingale optimal transport problem and proves stability.
result Stability of the extended problem with respect to risk-neutral marginal distributions.
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.
Optimal transport with scalar martingales defined over multiple periods.
problem Finding optimal transport plans with specific properties over multiple time periods.
method Introducing left-monotone transports and characterizing them through various properties.
result Left-monotone transports are unique under certain conditions and have specific order properties.
Tikhonov regularization is robust under specific martingale constraints in distributionally robust optimization.
problem Distributionally robust optimization and regularization of learning models.
method Optimal transport approach with martingale constraints.
result Tikhonov regularization is optimal transport robust under specified martingale constraints.
The study establishes stability in WMOT, crucial for finance with imprecise data.
problem Stability in weak martingale optimal transport for finance with imprecise data.
method Established stability through rigorous mathematical analysis.
result Stability of WMOT is proven, with applications to VIX futures and Brownian motion.
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.
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. Study optimal transport with backward martingale constraints in financial markets.
problem Optimal transport in financial markets with insider trading constraints.
method Maximal monotone set and minimal cost approach.
result Sharp conditions for uniqueness and representation of optimal transport plans.
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.
Study bounds financial path expectations using martingale distributions.
problem Bounding path-dependent financial expectations over martingale distributions.
method Relaxed martingale optimal transport problem, approximated via linear programming.
result Empirical relaxation can be approximated within O(n^(-1/2)) error.
Improved price bounds for financial derivatives using time-homogeneous stock movements.
problem Deriving robust price bounds for financial derivatives under time-homogeneous stock movements.
method Variant of martingale optimal transport problem with time-homogeneity assumption.
result Improved price bounds are derived, incorporating market data from multiple time points.
Study on convergence rates for optimal transport with regularization.
problem Convergence analysis of divergence-regularized optimal transport.
method Novel methodology using quantization and martingale couplings.
result Sharp rates for various divergences and transport costs.
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a…
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.
Gradient flow method solves for optimal transport starting distributions.
problem Finding the optimal starting distribution for a martingale in optimal transport.
method Following the gradient flow of the Bass functional's L2-lift.
result Gradient flow converges to a minimizer of the Bass functional.
We determine the optimal structure of couplings for the \emph{Martingale transport problem} between radially symmetric initial and terminal laws μ,ν on Rd and show the uniqueness of optimizer. Here optimality means that such solutions will minimize the functional $\E |X-Y|^p$ where 0<p≤1, and the dimensio…
The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints…
Unified RMOT framework for non-modelable risk factors reduces audit bounds.
problem Infinite audit bounds for exotic derivatives pricing with sparse market data.
method Rough Martingale Optimal Transport (RMOT) with rough volatility regularization.
result Finite, explicit, and asymptotically tight extrapolation bounds for non-modelable risk factors.
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.
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.
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.
Deep learning for financial derivatives pricing and hedging.
problem Model-free pricing and optimal hedging of financial derivatives.
method Neural networks for offline training and online application.
result Accurate model-free price bounds and optimal hedging strategies.
Paper reduces dimensionality for robust option pricing in 2-asset markets.
problem Robust option pricing in multi-asset markets with sub- or supermodular payoffs.
method Investigates the geometry of VMOT solutions, proving dimension reduction for 2 assets and developing a Sinkhorn algorithm.
result Dimension reduction to single-factor structure for 2-asset markets, significantly reducing computational time and improving accuracy.
In this paper we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two periods model. In particular, we consider the optimal transport plan constructed in \cite{HobsonKlimmek2013} as well as the one introduced in \cite{BeiglJuil} and further studi…
The study examines how including additional call option prices affects model-independent price bounds for exotic derivatives.
problem Improving model-independent price bounds for exotic derivatives using additional call option prices.
method Characterization of market settings that guarantee improved price bounds and exclusion of any improvement.
result The inclusion of additional call option prices can significantly impact model-independent price bounds.
Study optimizes financial strategies for various options globally.
problem Optimizing financial strategies for different types of options.
method Martingale optimal transport duality for càdlàg processes.
result Existence of robust semi-static superhedging strategies.
Dual representation of Kantorovich functional using martingale measures.
problem Representation of Kantorovich functional on Skorokhod space.
method Choquet capacity generated by martingale measures with constraints.
result Dual representation of Kantorovich functional.
A new relaxed framework for pricing illiquid derivatives using bid-ask spreads.
problem Pricing illiquid derivatives with realistic bounds and hedging prices.
method Introducing Bid--Ask Martingale Optimal Transport (BAMOT) that relaxes the exact calibration of model marginals to mid-prices of vanilla options.
result BAMOT yields realistic price bounds and superhedging prices for illiquid derivatives.
Study dynamic trading in options to improve price bounds for exotic derivatives.
problem Improving price bounds for exotic derivatives through dynamic option trading.
method Extend semi-static trading strategies to include dynamic option trading, analyze duality results and pricing rules.
result Improved price bounds for exotic derivatives compared to conventional methods.
Enhances MOT with causality constraints for better option pricing.
problem Limited applicability of traditional martingale optimal transport (MOT) for option pricing.
method Integrates causality constraints into MOT and proposes McCormick relaxations for computational tractability.
result Empirically, McCormick MOT yields significant price reductions for basket and digital options compared to classic MOT.
We prove dual attainment for multi-asset financial derivatives pricing.
problem Model-independent pricing and hedging of complex financial derivatives.
method Established duality and attained optimizers for multimarginal, multi-asset martingale optimal transport.
result Existence of dual optimizers under mild conditions for arbitrary numbers of assets and time periods.
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context suitable for martingale optimal transportation or, more generally, for optimal tra…
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the minimising pricing model for certain types of Asian options in discrete and continuous…
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present…
Study dynamic risk measures with distributional uncertainty using optimal transport.
problem Risk robustification under distributional uncertainty in Markovian models.
method Characterize risk measures via convex monotone semigroups and optimal transport costs.
result Identify generator and correction terms for dynamic risk measures under different scaling regimes.
Two new couplings for probability distributions are constructed and analyzed.
problem Constructing optimal couplings for two probability distributions.
method Optimizes constrained Monge-Kantorovich transport problems with supermartingales.
result Two new couplings are identified and characterized.