DOI10.1214/105051606000000169zbMath1142.91034arXivmath/0607111OpenAlexW2006080424MaRDI QIDQ997952
Laurent Denis, Claude Martini
Publication date: 8 August 2007
Published in: The Annals of Applied Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0607111
Term structure modeling under volatility uncertainty ⋮
Laws of large numbers under model uncertainty with an application to \(m\)-dependent random variables ⋮
Moral hazard under ambiguity ⋮
A \(\mathbb{C}^{0, 1}\)-functional Itô's formula and its applications in mathematical finance ⋮
Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications ⋮
Super-replication with nonlinear transaction costs and volatility uncertainty ⋮
Insurance pricing using \(H_{\infty}\)-control ⋮
Black-Scholes in a CEV random environment ⋮
Robust pricing-hedging dualities in continuous time ⋮
Strong limit theorems for extended independent random variables and extended negatively dependent random variables under sub-linear expectations ⋮
Robust valuation, arbitrage ambiguity and profit \& loss analysis ⋮
Dynamic programming principle for stochastic recursive optimal control problem driven by a \(G\)-Brownian motion ⋮
Robust utility maximization for a diffusion market model with misspecified coefficients ⋮
Multiple-priors optimal investment in discrete time for unbounded utility function ⋮
Random \(G\)-expectations ⋮
Robust maximization of asymptotic growth under covariance uncertainty ⋮
Backward stochastic differential equations driven by \(G\)-Brownian motion with double reflections ⋮
On representation theorem of sublinear expectation related to \(G\)-Lévy process and paths of \(G\)-Lévy process ⋮
General results on precise asymptotics under sub-linear expectations ⋮
Model uncertainty, recalibration, and the emergence of delta-vega hedging ⋮
Second order reflected backward stochastic differential equations ⋮
On the asymptotic approximation of inverse moment under sub-linear expectations ⋮
Quasi-sure exponential stabilization of stochastic systems induced by \(G\)-Brownian motion with discrete time feedback control ⋮
Probabilistic interpretation for solutions of fully nonlinear stochastic pdes ⋮
Partial super-hedging of derivatives with model risk ⋮
Second-order BSDEs with general reflection and game options under uncertainty ⋮
Optimal stopping under nonlinear expectation ⋮
Strong law of large numbers and Chover's law of the iterated logarithm under sub-linear expectations ⋮
Financial markets with volatility uncertainty ⋮
Reduced-form framework for multiple ordered default times under model uncertainty ⋮
Function spaces and capacity related to a sublinear expectation: application to \(G\)-Brownian motion paths ⋮
\(k\)-sample upper expectation linear regression-modeling, identifiability, estimation and prediction ⋮
Risk measuring under model uncertainty ⋮
Second order backward SDE with random terminal time ⋮
Dual formulation of second order target problems ⋮
Backward stochastic differential equations driven by \(G\)-Brownian motion ⋮
Wellposedness of second order backward SDEs ⋮
On conditional Chisini means and risk measures ⋮
ROBUST TRADING OF IMPLIED SKEW ⋮
Ambiguous volatility, possibility and utility in continuous time ⋮
A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options ⋮
The pricing of Asian options in uncertain volatility model ⋮
Constructing sublinear expectations on path space ⋮
Second order backward stochastic differential equations with quadratic growth ⋮
Viability for stochastic differential equations driven by \(G\)-Brownian motion ⋮
Martingale optimal transport and robust hedging in continuous time ⋮
Efficient hedging under ambiguity in continuous time ⋮
Optimal arbitrage under model uncertainty ⋮
No-arbitrage with multiple-priors in discrete time ⋮
A stochastic recursive optimal control problem under the G-expectation framework ⋮
Weak approximation of \(G\)-expectations ⋮
Three series theorem for independent random variables under sub-linear expectations with applications ⋮
Gambling for resurrection and the heat equation on a triangle ⋮
A Girsanov Type Theorem Under G-Framework ⋮
Hedging with small uncertainty aversion ⋮
Stochastic control for a class of nonlinear kernels and applications ⋮
Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation ⋮
An interval of no-arbitrage prices in financial markets with volatility uncertainty ⋮
Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm ⋮
Duality for pathwise superhedging in continuous time ⋮
Local time and Tanaka formula for the \(G\)-Brownian motion ⋮
Continuous-time trading and the emergence of probability ⋮
Superreplication under model uncertainty in discrete time ⋮
Martingale representation theorem for the \(G\)-expectation ⋮
Stopping times and related Itô's calculus with \(G\)-Brownian motion ⋮
The law of logarithm for arrays of random variables under sub-linear expectations ⋮
Arbitrage-free modeling under Knightian uncertainty ⋮
An efficient numerical method for forward-backward stochastic differential equations driven by \(G\)-Brownian motion ⋮
The \(CEV\) model and its application to financial markets with volatility uncertainty ⋮
Pathwise stochastic integrals for model free finance ⋮
Pathwise superhedging on prediction sets ⋮
A guaranteed deterministic approach to superhedging: financial market model, trading constraints, and the Bellman-Isaacs equations ⋮
UTILITY MAXIMIZATION UNDER MODEL UNCERTAINTY IN DISCRETE TIME ⋮
Complete convergence for widely acceptable random variables under the sublinear expectations ⋮
Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions ⋮
Lindeberg's central limit theorems for martingale like sequences under sub-linear expectations ⋮
Complete convergence for END random variables under sublinear expectations ⋮
Pathwise properties and homeomorphic flows for stochastic differential equations driven by \(G\)-Brownian motion ⋮
Another form of Chover's law of the iterated logarithm under sub-linear expectations ⋮
Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation ⋮
Good deal hedging and valuation under combined uncertainty about drift and volatility ⋮
Affine processes under parameter uncertainty ⋮
The functional Itō formula under the family of continuous semimartingale measures ⋮
The PDEs and numerical scheme for derivatives under uncertainty volatility ⋮
A complete representation theorem for G-martingales ⋮
Robust superhedging with jumps and diffusion ⋮
A unified framework for robust modelling of financial markets in discrete time ⋮
Second-order BSDEs with jumps: formulation and uniqueness ⋮
Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities ⋮
Retracted: Sublinear expectation nonlinear regression for the financial risk measurement and management ⋮
On representation theorem of \(G\)-expectations and paths of \(G\)-Brownian motion ⋮
Complete convergence for arrays of rowwise END random variables and its statistical applications under sub-linear expectations ⋮
Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations ⋮
Pathwise convergence under Knightian uncertainty ⋮
Reduced-form framework under model uncertainty ⋮
Optimal contracting under mean-volatility joint ambiguity uncertainties ⋮
Arbitrage and duality in nondominated discrete-time models ⋮
Minimal supersolutions of BSDEs under volatility uncertainty ⋮
The maximum maximum of a martingale with given \(n\) marginals ⋮
Universal arbitrage aggregator in discrete-time markets under uncertainty
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