Back to Search
Start Over
Parameter estimation of uncertain differential equation with application to financial market
- Source :
- Chaos, Solitons & Fractals. 139:110026
- Publication Year :
- 2020
- Publisher :
- Elsevier BV, 2020.
-
Abstract
- Uncertain differential equation (UDE) has been widely applied in the financial market, and many option pricing formulas are derived based on UDE. But the existing literature don’t consider the parameter estimation of UDE, and the parameters are just assumed as some given constants. This paper will present an approach to estimate the unknown parameter of UDE from discretely sampled data via α-path method for the first time. And the concepts of forecast value and confidence interval are introduced to predict the future value in a UDE. As five special UDEs, the parameters estimations of arithmetic Liu process, geometric Liu process, uncertain Ornstein-Uhlenbeck process, uncertain mean-reverting process, and uncertain exponential Ornstein-Uhlenbeck process are also derived, and the corresponding numerical examples are given. Furthermore, this paper proposes a means to estimate unknown parameters for the general geometric Liu process, and as an application, this method will be successfully used in Alibaba stock.
- Subjects :
- Estimation theory
Differential equation
General Mathematics
Applied Mathematics
Financial market
General Physics and Astronomy
Future value
Statistical and Nonlinear Physics
Uncertainty theory
01 natural sciences
Confidence interval
010305 fluids & plasmas
Exponential function
Valuation of options
0103 physical sciences
Applied mathematics
010301 acoustics
Mathematics
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 139
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi...........230c7454f4ef38f639d1c95b7e8b21fd