NUMERICAL SOLUTION OF A MATRIX INTEGRAL EQUATION ARISING IN MARKOV-MODULATED LEVY PROCESSES

被引：2

作者：

Bini, Dario ^{[1
]}

Latouche, Guy ^{[2
]}

Meini, Beatrice ^{[3
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

[2] Univ Libre Bruxelles, Dept DInformat, Cp212, B-1050 Brussels, Belgium

[3] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2022年 / 44卷 / 04期

关键词：

Markov modulation; Levy processes; nonlinear matrix equations; integral equations; numerical algorithms; fixed point iterations; POLYNOMIAL EQUATION; RISK PROCESS; 1ST PASSAGE; CONVERGENCE; RUIN;

D O I：

10.1137/21M1436543

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Markov-modulated Levy processes lead to matrix integral equations of the kind A(0) + A(1)X + A(2)X(2) + A(3)(X) = 0, where A(0), A(1), A(2) are given matrix coefficients, while A(3)(X) is a nonlinear function, expressed in terms of integrals involving the exponential of the matrix X itself. In this paper we propose some numerical methods for the solution of this class of matrix equations, perform a theoretical convergence analysis, and show the effectiveness of the new methods by means of a wide numerical experimentation.

引用

页码：A2669 / A2690

页数：22

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