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Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this paper, we present a rigorous proof for the convergence and error estimates of a free boundary problem modeling a credit rating migration. The high and low rating regions are characterized by different volatilities, $\\sigma_H$ and $\\sigma_L$, respectively. The high and low rating regions are separated by a free boundary. The changes in volatilities across the free boundary result in a discountinuity of the leading order coefficients, which implies that the solution will have a discontinuous second order spatial derivative across the free boundary; it is a challenge to establish convergence of a finite difference scheme for this type of solution. Through an approximation by smooth coefficients, energy estimates, delicate construction of super- and subsolutions, and establishment of a comparison principle, we prove $L^\\infty$ convergence of the explicit finite difference scheme. Furthermore, the convergence rate is of $\\frac{1}{4}$ order temporal accuracy and of $\\frac{1}{2}$ order spatial accuracy. To our best knowledge, this is the first work on convergence of a finite difference scheme for a rating migration problem.<\/jats:p>","DOI":"10.1137\/17m1151833","type":"journal-article","created":{"date-parts":[[2018,8,7]],"date-time":"2018-08-07T12:19:05Z","timestamp":1533644345000},"page":"2430-2460","source":"Crossref","is-referenced-by-count":8,"title":["Convergence Rate of an Explicit Finite Difference Scheme for a Credit Rating Migration Problem"],"prefix":"10.1137","volume":"56","author":[{"given":"Yan","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengce","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bei","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,8,7]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2002002"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/S003614290343815X"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-02000-5"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/090761501"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/080723144"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2016004"},{"key":"atypb7","first-page":"108","volume":"17","author":"Dong H. 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