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.
Neural networks approximate superhedging prices in financial models.
problem Approximating superhedging prices in financial markets.
method Neural networks for approximating α-quantile hedging prices and their essential supremum. result Neural networks provide an approximation for superhedging prices and strategies.
We establish a nondominated version of the optional decomposition theorem in a setting that includes jump processes with nonvanishing diffusion as well as general continuous processes. This result is used to derive a robust superhedging duality and the existence of an optimal superhedging strategy for general contingen…
Study pricing and hedging for American options in a market with default risk.
problem Pricing and hedging American options in a market with default risk.
method Defines seller's and buyer's superhedging prices using optimal stopping problems and nonlinear expectations.
result Seller's and buyer's superhedging prices coincide and are characterized by nonlinear reflected BSDEs.
Revisits superhedging under proportional costs in continuous time markets.
problem Superhedging in markets with proportional transaction costs.
method Set-valued stochastic analysis, continuous trading schemes, dynamic risk measure.
result Dynamic set-valued risk measure with multi-portfolio time-consistency.
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive construction involving set operations, going backward in the event tree. We ref…
New robust estimators for superhedging prices in financial markets.
problem Lack of robustness in existing statistical estimation methods for superhedging prices.
method Introduced novel estimators using martingale measures with tradeoffs between empirical measures and martingale densities.
result Established consistency and robustness of the new estimators, offering superior performance compared to the plugin estimator.
We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family P of possible physical measures. A robust notion NA1(P) of no-arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot …
Continuous-time pricing-hedging duality for European options.
problem Finding the minimal superhedging price of path-dependent European options.
method Formulates a duality between analytic and probabilistic problems, using simple trading strategies and semi-continuous claims.
result The minimal superhedging price equals the supremum of expectations over all martingale measures.
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strate…
Study pricing game options in imperfect markets with default.
problem Pricing game options in markets with default and imperfections.
method Extend Kifer's results to imperfect markets, introduce seller's price, prove equivalence to Dynkin game value function.
result Seller's price equals the value function of a generalized Dynkin game under nonlinear expectation.
A trader optimizes robust superhedging under subjective market views.
problem Optimizing robust superhedging with subjective market views.
method Dynamic programming and robust maximization under new measures.
result Existence and uniqueness of optimal investment and consumption strategies.
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading strategy in risky assets …
In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path ω∈Ω, might be strictly greater than the …
We construct algorithms for computation of prices and superhedging strategies for game options in general discrete markets both from the seller and the buyer points of view.
Study investigates duality and dual optimizers for various transport problems.
problem Existence and characterization of dual optimizers for adapted transport problems.
method Minimal assumptions, including causal and bicausal settings, are considered.
result No-arbitrage assumption leads to multicausal couplings and equivalent robust superhedging price computation.
We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measur…
New method for pricing and hedging options in risky markets.
problem Pricing and hedging derivatives in markets with equivalent local martingale measures not existing.
method Introduces a new superhedging duality for American options in a general market setting.
result Answers a question raised by Fernholz, Karatzas, and Kardaras about pricing American options.
In a continuous-time model with multiple assets described by càdlàg processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality bet…
Solves superhedging for European options in a model with transient price impact and settlement requirements.
problem Superhedging European options in a model with transient price impact and settlement requirements.
method Analyzes geometric dynamic programming with reduced effective coordinates, considering non-linear price impact and resilience functions.
result Viscosity solutions describe minimal superhedging prices, governed by transient price impact and settlement specifications.
Paper establishes robust asset pricing theorems under uncertainty.
problem Tackles asset pricing in uncertain discrete time settings.
method Introduces a new topological framework for Lp spaces and functional analysis. result Equivalence of robust no arbitrage condition and robust pricing system existence.
The study provides a practical strategy for pricing and hedging equity-release mortgages guarantees.
problem Pricing and hedging the No-Negative-Equity-Guarantee in incomplete markets.
method Discrete-time model, Excess-of-Loss reinsurance, numerical illustrations.
result Superhedge cost decreases with more lives in the portfolio, making it more realistic.
Agent-based model for two stocks using superhedging.
problem Modeling price evolution of two stocks with operational rebalancing.
method Agent-based modeling with dynamic programming and graph data structure.
result Validates risk-reward profiles through superhedging and underhedging bounds.
The paper offers a pricing-hedging method for prediction sets.
problem Model-independent superhedging with pathwise constraints.
method Pathwise superhedging on prediction sets with respect to martingale measures.
result The superhedging price equals the supremum of pricing functionals over measures concentrated on the prediction set.
Study proves duality in exotic option pricing under uncertain model and delayed information.
problem Pricing and hedging of multi-action exotic options under nondominated model uncertainty and delayed information.
method Reformulated superhedging problem as a European option problem, proving duality results.
result Superhedging price equals model-based price with future look-up power.
The study analyzes financial markets with transaction costs and proves asset pricing theorems.
problem Model-independent financial markets with proportional transaction costs.
method Develops a Fundamental and Superhedging Theorem, proving equivalence to Consistent Price Systems.
result The superhedging price in the presence of transaction costs matches the frictionless case for a suitable process.
Game options study gradual exercise and cancellation with transaction costs.
problem Analyzing game options with gradual exercise and cancellation under proportional transaction costs.
method Developed algorithmic constructions for bid and ask prices, superhedging strategies, and optimal mixed stopping times.
result Increased flexibility in hedging leads to tighter bounds on option price.
Formulates superhedging under costs and uncertainty for continuous assets.
problem Superhedging with transaction costs and model uncertainty for continuous processes.
method New topological framework for continuous asset prices with parametric model uncertainty.
result Formulates a superhedging theorem in the presence of transaction costs and model uncertainty.
A new method for stochastic integration using superhedging.
problem Existence of quadratic variation in stochastic processes.
method Using Vovk's outer measure to show the existence of quadratic variation for typical price paths.
result Developed a model-free Itô integration method based on robust quadratic variation.
New method for superhedging without assuming continuous claims.
problem Superhedging without assuming upper semicontinuous contingent claims.
method Established a generalized duality for model-free superhedging using Choquet's capacitability theorem.
result Generalized duality for superhedging given marginal distributions without continuity assumptions.
Investor optimizes worst case exponential utility in uncertain markets with unbounded endowments.
problem Maximizing worst case exponential utility in uncertain financial markets with unbounded endowments.
method Dynamic investment strategy and static option investment, using martingale measures and dual representation.
result Optimal strategy exists and convergence to robust superhedging price as risk aversion increases.
Unified approach to financial market modeling in discrete time.
problem Establishing equivalence between pathwise and quasi-sure approaches.
method Unified framework proving Fundamental and Superhedging Theorems.
result Unified approach encompasses and clarifies different notions of arbitrage.
Extends reduced-form models to model uncertainty, studying superhedging in continuous time.
problem Model uncertainty in financial markets, particularly credit and insurance.
method Sublinear conditional expectation with respect to a family of probability measures.
result Established equivalent versions of dynamic robust superhedging duality.
The paper proves superhedging duality with transaction costs and frictions.
problem Superhedging under proportional transaction costs and model uncertainty.
method Quasi-sure setup with solvency cones, removing restrictive assumptions.
result Duality proved under more natural conditions of No Strict Arbitrage.
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…
We propose a new non parametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove some optimal statistical properties of our estimates. As an application we firs…
New method for practical hedging under uncertainty in continuous time models.
problem High minimal superhedging price for practical use in continuous-time models.
method Relaxed hedging criterion based on acceptable shortfall risks, combining aggregation and convex dual representation theorems.
result Derivation of duality results for minimal price on discounted claims.
Improved bounds for multi-asset options using deep learning and market prices.
problem Computing model-free bounds for multi-asset options with uncertainty in dependence structure.
method Fundamental theorem of asset pricing, superhedging duality, penalization approach, deep learning.
result Deep learning approximations improve computational efficiency and accuracy.
Optimizes risk management in incomplete markets using convex risk measures.
problem Risk management in financial markets with incomplete information.
method Dynamic optimization problem split into static and representation problems; convex duality methods used.
result Optimal strategy involves superhedging a modified claim with a randomized test.
Paper proves game-theoretic and measure-theoretic expectations match for a specific financial scenario.
problem Proving equivalence between game-theoretic and measure-theoretic probability.
method New broad definition of game-theoretic probability; proving coincidence of expectations for lower semicontinuous positive functionals.
result Coincidence of game-theoretic and measure-theoretic expectations for specific financial scenario.
This paper finds bounds on the price of LETF options using a new optimal solution to the Skorokhod embedding problem.
problem Finding model-free bounds on the price of European options on a leveraged ETF.
method Establishing a new optimal solution to the Skorokhod embedding problem (SEP) using methods from Beiglböck-Cox-Huesmann, and characterizing the optimal stopping region.
result The paper provides the first solution to the SEP where the optimal region is not uniquely characterised by its geometric structure, requiring an additional condition.
American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomised) stopping time. The introduction of gradual exercise leads to tighter bounds on the option price when compared to the …
We study superhedging of contingent claims with physical delivery in a discrete-time market model with convex transaction costs. Our model extends Kabanov's currency market model by allowing for nonlinear illiquidity effects. We show that an appropriate generalization of Schachermayer's robust no arbitrage condition im…
Extends classical model of transaction costs to convex costs and multivariate positions.
problem Risk arbitrage and hedging under transaction costs with convex costs and multivariate positions.
method Extends classical model to convex transaction costs and multivariate acceptable positions, using results for unbounded and non-closed random sets.
result Formulates no arbitrage conditions and explores their connections, leading to a decrease in superhedging prices.
This paper examines pricing and hedging strategies for cross-currency equity protection swaps.
problem Dynamic requirements from EPS buyers in cross-currency equity protection swaps.
method Detailed analysis of two hedging paradigms, including separate and aggregated returns, with consideration of different types of returns.
result Proposes various hedging strategies with practical implications for EPS providers and investors.
We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). I…
Maximizes American put price bounds using European put prices.
problem Finding upper bounds for American put prices.
method Model-free approach using European put prices and martingale transport.
result Derives a model with maximal American put price.
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.