The Riccati Equation in Mathematical Finance

@article{Boyle2002TheRE,
  title={The Riccati Equation in Mathematical Finance},
  author={Phelim P. Boyle and Wenwen Tian and Fred Guan},
  journal={J. Symb. Comput.},
  year={2002},
  volume={33},
  pages={343-355}
}
This paper uses ideas from symbolic computation to classify solutions to an important class of problems in mathematical finance and thus provides a linkage between these two fields. We show that Kovacic?s concept of closed-form solutions to the Riccati ordinary differential equation can be used to provide a precise mathematical definition that is useful in certain financial models. We extend this definition to a broader class of problems and discuss how these ideas can be usefully applied to… 
View via Publisher
27 Citations
Background Citations
9
Methods Citations
5

27 Citations

A study of the solution to the Riccati equation in term structure modelling
We study numerical (i.e. approximate) and analytical (i.e. exact) solutions to the system of Riccati ordinary differential equations (RODE) used in estimating the class of Gaussian affine term…
Formulas For Solutions Of The Riccati’s Equation
In this paper we obtained the formula for the common solution of Riccati equations. Here Riccati equations was solved for common cases. Results obtained have been compared with the conventional ones…
On matching diffusions, Laplace transforms and partial differential equations
Fractional neural network models for nonlinear Riccati systems
In this article, strength of fractional neural networks (FrNNs) is exploited to find the approximate solutions of nonlinear systems based on Riccati equations of arbitrary order. The feed-forward…
Classes of elementary function solutions to the CEV model I
  • E. Melas
  • Mathematics
    J. Comput. Appl. Math.
  • 2019
A unified approach to explicit bond price solutions under a time-dependent affine term structure modelling framework
The richness and simplicity in the econometric specification of interest rate dynamics are the main motivations why affine term structure models (ATSMs) continue to be popular nowadays. Analytic…
Exact Pricing of Asian Options: An Application of Spectral Theory
Arithmetic Asian or average price (rate) options deliver payoffs based on the average underlying price over a pre-speciÞed time period. Asian options are an important family of derivative contracts…
Formulas for solution of Riccati's equationle
  • A. Asanov, E. Hazar, R. Asanov
  • Mathematics
    2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON)
  • 2017
In this paper we obtained the formula for the common solution of Riccati equations. Here Riccati equations was solved for common cases. Results obtained have been compared with the conventional ones…
Approximate solution for solving fractional Riccati differential equations via trigonometric basic functions
  • B. Agheli
  • Mathematics
    Transactions of A. Razmadze Mathematical Institute
  • 2018
Computation of optimal portfolios using simulation-based dimension reduction
...
...

References

SHOWING 1-10 OF 28 REFERENCES
A Theory for the Term Structure of Interest Rates
TLDR
The discretised theoretical distributions matching the empirical data from the Federal Reserve System are deduced from aDiscretised seed which enjoys remarkable scaling laws and may be used to develop new methods for the computation of the value-at-risk and fixed-income derivative pricing.
An equilibrium characterization of the term structure
Dynamic Asset Pricing Theory
"Dynamic Asset Pricing Theory" is a textbook for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing…
Pricing Interest-Rate-Derivative Securities
This article shows that the one-state-variable interest-rate models of Vasicek (1977) and Cox, Ingersoll, and Ross (1985b) can be extended so that they are consistent with both the current term…
A Yield-factor Model of Interest Rates
  • N. Ka
  • Mathematics, Economics
  • 1996
This paper presents a consistent and arbitrage-free multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric multivariate Markov…
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and…
Integration of Transcendental Functions
TLDR
This chapter defines formally the integration problem in an algebraic setting, proves the main theorem of symbolic integration (Liouville’s Theorem), and describes the main part of the integration algorithm.
A simple class of square-root interest-rate models
An analytically tractable class of square-root interest-rate models is introduced. Algebraic expressions are found for the drift and volatility parameters of the short rate in terms of initial yield…
Some tapas of computer algebra
  • A. Cohen
  • Mathematics
    Algorithms and computation in mathematics
  • 1999
Grbner bases, an introduction, A.M. Cohen symbolic recipes for polynomial system solving, L. Gonzalez-Vega et al lattice reduction, F. Beukers factorization of polynomials, F. Beukers computation in…
Symbolic integration I: transcendental functions
...
...