Large deviations for some fast stochastic volatility models by viscosity methods

DOI10.3934/dcds.2015.35.3965zbMath1332.93265arXiv1405.3206OpenAlexW2950209415MaRDI QIDQ255794

Annalisa Cesaroni, Martino Bardi, Daria Ghilli

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.3206

zbMATH Keywords

stochastic volatilitysingular perturbationslarge deviationsviscosity solutions

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Time-scale analysis and singular perturbations in control/observation systems (93C70) Large deviations (60F10) Derivative securities (option pricing, hedging, etc.) (91G20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items

Sharp estimates of the generalized principal eigenvalue for superlinear viscous Hamilton-Jacobi equations with inward drift ⋮ Viscosity methods for large deviations estimates of multiscale stochastic processes ⋮ Rate of convergence for singular perturbations of Hamilton-Jacobi equations in unbounded spaces ⋮ Property and numerical simulation of the Ait-Sahalia-Rho model with nonlinear growth conditions ⋮ Comparison principle for Hamilton-Jacobi-Bellman equations via a bootstrapping procedure ⋮ A priori Lipschitz estimates for solutions of local and nonlocal Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large deviations for multiscale diffusion via weak convergence methods
• Optimal control with random parameters: a multiscale approach
• Small-time asymptotics for fast mean-reverting stochastic volatility models
• Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations
• Large deviations for two-time-scale diffusions, with delays
• A remark on a singular perturbation method for option pricing under a stochastic volatility model
• A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities
• Weak convergence methods and singularly perturbed stochastic control and filtering problems
• Viscosity solutions of Hamilton-Jacobi equations
• Singular perturbations of nonlinear degenerate parabolic pDEs: A general convergence result
• Application of large deviation methods to the pricing of index options in finance.
• On large deviations for SDEs with small diffusion and averaging.
• Large deviations for two scaled diffusions
• Large deviations and importance sampling for systems of slow-fast motion
• Multiscale problems and homogenization for second-order Hamilton-Jacobi equations
• Controlled Markov processes and viscosity solutions
• On the structure of solutions of ergodic type Bellman equation related to risk-sensitive control
• Homogenization and Vanishing Viscosity in Fully Nonlinear Elliptic Equations: Rate of Convergence Estimates
• Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
• Uniqueness Results for Second-Order Bellman--Isaacs Equations under Quadratic Growth Assumptions and Applications
• Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations
• Short-Maturity Asymptotics for a Fast Mean-Reverting Heston Stochastic Volatility Model
• Convergence by Viscosity Methods in Multiscale Financial Models with Stochastic Volatility
• Probability with Martingales
• On ergodic stochastic control
• Singular Perturbations in Option Pricing
• Value functions for Bolza problems with discontinuous Lagrangians and Hamilton-Jacobi inequalities
• Viscosity Solutions Methods for Singular Perturbations in Deterministic and Stochastic Control
• Multiscale Stochastic Volatility Asymptotics
• The perturbed test function method for viscosity solutions of nonlinear PDE
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

This page was built for publication: Large deviations for some fast stochastic volatility models by viscosity methods