2017/03/01 by Daniel Kreßner, Kressner, Daniel, Robert Luce +3
Business, Management and Accounting · Computer Science · Economics, Econometrics and Finance · #15A16 #65F60 #91G20 #Advanced Queuing Theory Analysis #FOS: Economics and business #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1703.00182
openalex publication_date 2017/03/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/08/01
We study the problem of computing the matrix exponential of a block\ntriangular matrix in a peculiar way: Block column by block column, from left to\nright. The need for such an evaluation scheme arises naturally in the context\nof option pricing in polynomial diffusion models. In this setting a\ndiscretization process produces a sequence of nested block triangular matrices,\nand their exponentials are to be computed at each stage, until a dynamically\nevaluated criterion allows to stop. Our algorithm is based on scaling and\nsquaring. By carefully reusing certain intermediate quantities from one step to\nthe next, we can efficiently compute such a sequence of matrix exponentials.\n