An optimal system and group-invariant solutions of the Cox-Ingersoll-Ross pricing equation

DOI10.1016/j.amc.2007.12.008zbMath1142.91466OpenAlexW2040524785MaRDI QIDQ945217

B. E. Eshmatov

Publication date: 12 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.12.008

zbMATH Keywords

Lie algebrapartial differential equationsoptimal systeminterest rate derivativesCIR

Mathematics Subject Classification ID

Microeconomic theory (price theory and economic markets) (91B24) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Lie algebras and Lie superalgebras (17B99)

Related Items (16)

Algebraic resolution of equations of the Black-Scholes type with arbitrary time-dependent parameters ⋮ Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance ⋮ A terminal condition in linear bond-pricing under symmetry invariance ⋮ Lie symmetry analysis, exact solutions, conservation laws of variable-coefficients Calogero–Bogoyavlenskii–Schiff equation ⋮ Symmetry-based optimal portfolio for a DC pension plan under a CEV model with power utility ⋮ Group classification of a general bond-option pricing equation of mathematical finance ⋮ Lie symmetry analysis of the Black-Scholes-Merton model for European options with stochastic volatility ⋮ Generalized uncorrelated SABR models with a high degree of symmetry ⋮ Two ways to solve, using Lie group analysis, the fundamental valuation equation in the double-square-root model of the term structure ⋮ A note on the integrability of the classical portfolio selection model ⋮ Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility ⋮ SOLVING THE ASIAN OPTION PDE USING LIE SYMMETRY METHODS ⋮ Embedding the Vasicek model into the Cox-Ingersoll-Ross model ⋮ Lie theory: Applications to problems in mathematical finance and economics ⋮ Symmetry analysis for Whitham-Broer-Kaup equations ⋮ The algebraic properties of the space-and time-dependent one-factor model of commodities

Uses Software

• Mathematica
• SYMMGRP
• LIE

Cites Work

• Lie symmetry analysis of differential equations in finance
• Review of symbolic software for Lie symmetry analysis
• Optimal system and group invariant solutions for a nonlinear wave equation.
• Pricing multi-asset financial derivatives with time-dependent parameters -- Lie algebraic approach
• An Intertemporal General Equilibrium Model of Asset Prices
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• The Mathematics of Financial Derivatives
• Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries
• LIE, a PC program for Lie analysis of differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: An optimal system and group-invariant solutions of the Cox-Ingersoll-Ross pricing equation