The previous uncertain chemical reaction equation describes the time evolution of single reactions. But in many practical cases, a substance is consumed by several different reaction pathways. For the above considerations, this paper extends the discussion to multiple reactions. Specifically, by taking the decomposition of C2H5OH as an example, parallel reactions with one reactant are analyzed with the multifactor uncertain differential equation. The derived equation is called the multifactor uncertain chemical reaction equation. Following that, the parameters in the multifactor uncertain chemical reaction equation are estimated by the generalized moment estimation. Based on the multifactor uncertain chemical reaction equation, half-life of reaction is investigated. Finally, a numerical example is presented to illustrate the usefulness of the multifactor uncertain chemical reaction equation.
Abstract
Traditional finance studies of credit risk structured models are based on the assumption that the price of the underlying asset obeys a stochastic differential equation. However, according to behavioral finance, the price of the underlying asset is not entirely stochastic, and the credibility of financial investors also plays a very important role in asset prices. In this paper we introduce uncertainty theory to describe these credibility of investors and propose a new credit risk structured model with jumps based on the assumption that the underlying asset is described by an uncertain differential equation with jumps. The company default belief degree formula, zero coupon bond value and stock value formula are formulated. Company bond credit spread and credit default swap (CDS) pricing are studied as applications of the proposed model in uncertain markets.
The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor uncertain differential equation by considering the external noise and internal noise in an actual electrical circuit system. Then, the solution of uncertain RL circuit equation and the inverse uncertainty distribution of solution are derived. Some applications of solution for uncertain RL circuit equation are also investigated. Finally, the method of moments is used to estimate the unknown parameters in uncertain RL circuit equation.
In uncertainty theory, parameter estimation of uncertain differential equation is a very important research direction. The parameter estimation of multifactor uncertain differential equation needs to be solved. Multifactor uncertain differential equation is a differential equation driven by multiple Liu processes. The paper introduces two methods to solve the unknown parameters of the multifactor uncertain differential equation, they are the method of moment estimation and the method of least squares estimation. Several numerical examples are used to illustrate the proposed parameter estimation methods.
Parameter estimation of high-order uncertain differential equations is an inevitable problem in practice. In this paper, the equivalent equations of high-order uncertain differential equations are obtained by transformation, and the parameters of the first-order uncertain differential equation including Liu process are estimated. Based on the least squares estimation method, this paper proposes a means to minimize the residual sum of squares to obtain an estimate of the parameters in the drift term, and make the noise sum of squares equal to the residual sum of squares to obtain an estimate of the parameters in the diffusion term. In addition, some numerical examples are given to illustrate the proposed method. Finally, applications of the high-order uncertain spring vibration equations verify the viability of our method.
This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.
Uncertain statistics is a set of mathematical techniques for collecting, analyzing and interpreting data by uncertainty theory. In this paper, the main topics of uncertain statistics, including estimation of uncertainty distribution, uncertain regression analysis, uncertain times series, uncertain differential equation and uncertain hypothesis test, are reviewed. Furthermore, by the application to the COVID-19 spread in China, the advantages of those techniques in uncertain statistics are sorted out.
Interest rate, stock and option are all important parts of finance. This paper introduces uncertain differential equation to study the evolution of interest rate and stock price separately. Based on actual observations, we estimate the parameters in uncertain differential equation with the method of moments. Using the introduced interest rate and stock models, we price European options and compare the results pricing with actual observations. Finally, a paradox of the stochastic financial model is stated.
Structural Credit Risk Model with Jumps Based on Uncertainty Theory
