英文标题：
《Incremental computation of block triangular matrix exponentials with
application to option pricing》
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作者：
Daniel Kressner, Robert Luce, Francesco Statti
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最新提交年份：
2017
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英文摘要：
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomial diffusion models. In this setting a discretization process produces a sequence of nested block triangular matrices, and their exponentials are to be computed at each stage, until a dynamically evaluated criterion allows to stop. Our algorithm is based on scaling and squaring. By carefully reusing certain intermediate quantities from one step to the next, we can efficiently compute such a sequence of matrix exponentials.
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中文摘要：
我们以一种特殊的方式研究了块三角矩阵的矩阵指数的计算问题：从左到右逐块列计算。在多项式扩散模型中的期权定价背景下，这种评估方案的需要自然产生。在此设置中，离散化过程生成一系列嵌套块三角矩阵，并在每个阶段计算其指数，直到动态评估的标准允许停止。我们的算法基于缩放和平方。通过从一步到下一步仔细地重用某些中间量，我们可以有效地计算这样一系列矩阵指数。
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分类信息：

一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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