A theoretical framework for the pricing of contingent claims in the presence of model uncertainty

Abstract

The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a generalization of the uncertain volatility model (UVM) introduced in by Avellaneda, Levy and Paras. The uncertainty is specified by a family of martingale probability measures which may not be dominated. We obtain a partial characterization result and a full characterization which extends Avellaneda, Levy and Paras results in the UVM case.

Published at http://dx.doi.org/10.1214/105051606000000169 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (79)

• Arbitrage and duality in nondominated discrete-time models
• Martingale Representation Theorem for the G-expectation
• Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications
• A New Central Limit Theorem under Sublinear Expectations
• A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Dual formulation of second order target problems
• Constructing Sublinear Expectations on Path Space
• Exponential inequalities under sub-linear expectations with applications to laws of the iterated logarithm
• Random G-expectations
• Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm
• Continuous-time trading and the emergence of probability
• Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
• A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations
• Stochastic differential equations driven by $G$-Brownian motion with reflecting boundary conditions
• Pathwise Construction of Stochastic Integrals
• The maximum maximum of a martingale with given $n$ marginals
• Pathwise stochastic integrals for model free finance
• Optimal arbitrage under model uncertainty
• Second order reflected backward stochastic differential equations
• G-Lévy Processes under Sublinear Expectations
• Tightness, weak compactness of nonlinear expectations and application to CLT
• A Complete Representation Theorem for $G$-martingales
• Local time and Tanaka formula for G-Brownian Motion
• Backward Stochastic Differential Equations Driven by G-Brownian Motion
• Second-order BSDEs with jumps: Formulation and uniqueness
• Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations
• Lindeberg's central limit theorems for martingale like sequences under sub-linear expectations
• Extended Conditional G-Expectations and Related Stopping Times
• Optimal Stopping under Nonlinear Expectation
• Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion
• Dynamic Programming Principle for Stochastic Recursive Optimal Control Problem under G-framework
• On the Robust superhedging of measurable claims
• Ambiguous Volatility, Possibility and Utility in Continuous Time
• Reduced-form framework under model uncertainty
• Viscosity Solutions of Fully Nonlinear Elliptic Path Dependent PDEs
• Wellposedness of Second Order Backward SDEs
• A unified Framework for Robust Modelling of Financial Markets in discrete time
• Robust Optimal Investment in Discrete Time for Unbounded Utility Function
• An extension of the functional Ito formula under a family of non-dominated measures
• Robust maximization of asymptotic growth under covariance uncertainty
• Coherent Price Systems and Uncertainty-Neutral Valuation
• $G$-martingale representation in the $G$-L'evy setting
• G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics
• On robust pricing-hedging duality in continuous time
• Robust Fundamental Theorem for Continuous Processes
• Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty
• Martingale Optimal Transport and Robust Hedging in Continuous Time
• Intertemporal Cost-efficient Consumption
• G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE
• Superreplication under Model Uncertainty in Discrete Time
• On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion
• Weak Approximation of G-Expectations
• Some Norm Estimates for Semimartingales
• Duality and approximation of stochastic optimal control problems under expectation constraints
• A stochastic recursive optimal control problem under the G-expectation framework
• A variational representation and large deviations for functionals of G-Brownian motion
• On the properites of Poisson random measures associated with a G-Levy process
• Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *
• Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections
• A $C^{0,1}$-functional Itô's formula and its applications in mathematical finance
• Second Order Backward Stochastic Differential Equations with Quadratic Growth
• Stochastic optimal control problem with infinite horizon driven by G-Brownian motion
• Harnack Inequality and Gradient Estimate for $G$-SDEs with Degenerate Noise
• A note on pricing of contingent claims under G-expectation
• Three series theorem for independent random variables under sub-linear expectations with applications
• Convergence of utility indifference prices to the superreplication price in a multiple-priors framework
• Utility Maximization under Model Uncertainty in Discrete Time
• Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
• Minimal supersolutions of BSDEs under volatility uncertainty
• Robust valuation and risk measurement under model uncertainty
• Multi-dimensional reflected BSDEs driven by $G$-Brownian motion with diagonal generators
• Second Order Backward Stochastic Differential Equations under Monotonicity Condition
• The Value of Insider Information for Super--Replication with Quadratic Transaction Costs
• Model reduction and uncertainty quantification of multiscale diffusions with parameter uncertainties using nonlinear expectations
• Ambiguous volatility and asset pricing in continuous time
• Some Results on Skorokhod Embedding and Robust Hedging with Local Time
• Robust Trading of Implied Skew
• Hedging of Game Options under Model Uncertainty in Discrete Time