Symmetry analysis of a model of stochastic volatility with time-dependent parameters

DOI10.1016/j.cam.2011.03.009zbMath1231.91493OpenAlexW2047171476MaRDI QIDQ548314

Yong-Cai Geng, Sumit K. Garg

Publication date: 28 June 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.03.009

zbMATH Keywords

stochastic processessymmetriesnonlinear evolution equations

Mathematics Subject Classification ID

Martingales with continuous parameter (60G44) Financial applications of other theories (91G80) Initial value problems for second-order parabolic equations (35K15) Self-similar solutions to PDEs (35C06)

Related Items (8)

Algebraic resolution of equations of the Black-Scholes type with arbitrary time-dependent parameters ⋮ Solving a partial differential equation associated with the pricing of power options with time‐dependent parameters ⋮ Option pricing: the reduced-form SDE model ⋮ Symmetry-based optimal portfolio for a DC pension plan under a CEV model with power utility ⋮ Lie symmetries of generalized Burgers equations: application to boundary-value problems ⋮ Application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition ⋮ Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility ⋮ Exact solutions via equivalence transformations of variable-coefficient fifth-order KdV equations

Uses Software

• REDUCE
• SYM
• LIE

Cites Work

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• Algebraic solution of the Stein-Stein model for stochastic volatility
• Invariance properties of a general bond-pricing equation
• On the systematic approach to the classification of differential equations by group theoretical methods
• Lie symmetry analysis of differential equations in finance
• Integration of second order ordinary differential equations not possessing Lie point symmetries
• Symmetry-based solution of a model for a combination of a risky investment and a riskless investment
• Symmetry, Singularities and Integrability in Complex Dynamics V: Complete Symmetry Groups of Certain Relativistic Spherically Symmetric Systems
• The density process of the minimal entropy martingale measure in a stochastic volatility market. A PDE Approach
• Nonlocal Symmetries and the Complete Symmetry Group of 1 + 1 Evolution Equations
• Time Dependent Heston Model
• Exponential nonlocal symmetries and nonnormal reduction of order
• A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets
• Symmetry Reductions of a Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Stock Price Distributions with Stochastic Volatility: An Analytic Approach
• Zero‐coupon bond prices in the Vasicek and CIR models: Their computation as group‐invariant solutions
• Algebraic properties of evolution partial differential equations modelling prices of commodities
• Complete Specification of Some Partial Differential Equations That Arise in Financial Mathematics
• LIE, a PC program for Lie analysis of differential equations

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