Technical Note-On Matrix Exponential Differentiation with Application to Weighted Sum Distributions

• 成果类型: Article
• 署名作者: Das, Milan Kumar; Tsai, Henghsiu; Kyriakou, Ioannis; Fusai, Gianluca
• 署名单位: Academia Sinica - Taiwan; City St Georges, University of London; University of Eastern Piedmont Amedeo Avogadro; City St Georges, University of London
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2257
• 发表日期: 2022
• 关键词: stochastic sum; probability distribution; matrix exponential and column vector differentiation; Pearson curve fi; pricing

摘要

In this note, we revisit the innovative transform approach introduced by Cai, Song, and Kou [(2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3):540???554] for accurately approximating the probability distribution of a weighted stochastic sum or time integral under general one-dimensional Markov processes. Since then, Song, Cai, and Kou [(2018) Computable error bounds of Laplace inversion for pricing Asian options. INFORMS J. Comput. 30(4):625???786] and Cui, Lee, and Liu [(2018) Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes. Eur. J. Oper. Res. 266(3):1134???1139] have achieved an efficient reduction of the original double to a single-transform approach. We move one step further by approaching the problem from a new angle and, by dealing with the main obstacle relating to the differentiation of the exponential of a matrix, we bypass the transform inversion. We highlight the benefit from the new result by means of some numerical examples.