Convex Quadratic Optimization Based on Generator Matrix in Credit Risk Transfer Process

Liping Zhang

doi:https://doi.org/10.14445/22315373/IJMTT-V65I3P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 3 | Year 2019 | Article Id. IJMTT-V65I3P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I3P515

Convex Quadratic Optimization Based on Generator Matrix in Credit Risk Transfer Process

Liping Zhang

Citation :

Liping Zhang, "Convex Quadratic Optimization Based on Generator Matrix in Credit Risk Transfer Process," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 3, pp. 92-106, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I3P515

Abstract

In this paper, the generator matrix is calculated based on the grade transfer matrix over a period of time in the quantitative analysis of credit risk, which has become one of the hot issues that many scholars pay attention to and study.From the mathematical model point of view combined with the actual situation, the calculation of the generated matrix can be regarded as optimization problems of the matrix logarithm. This article is based on Prof Kreinin and Prof Sidelnikova’s classical optimization model, and we use the combination model of Markov chain and the effective set method of convex quadratic optimization to solve the problem. We mainly make the feasible domain satisfy the applicable conditions by reducing dimensions and correcting variables and theoretically verify the convergence and feasibility of the optimization system. Meanwhile, we verify the data published by Standard and Poor’s Credit Review by Matlab.

Keywords

credit risk, convex quadratic optimization, effective set method, generator matrix, Markov chain

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