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

Das, M. K., Tsai, H., Kyriakou, I. ORCID: 0000-0001-9592-596X & Fusai, G. ORCID: 0000-0001-9215-2586 (2022). Technical Note - On Matrix Exponential Differentiation with Application to Weighted Sum Distributions. Operations Research, doi: 10.1287/opre.2021.2257

Abstract

In this note, we revisit the innovative transform approach introduced by Cai et al. [Cai, N., Song, Y., Kou, S., 2015. A general framework for pricing Asian options under Markov processes] for accurately approximating the probability distribution of a weighted stochastic sum or time integral under general one-dimensional Markov processes. Since then, Song et al. [Song, Y., Cai, N., Kou, S., 2018. Computable error bounds of Laplace inversion for pricing Asian options] and Cui et al. [Cui, Z., Lee, C., Liu, Y., 2018. Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes] 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.

Publication Type: Article
Additional Information: This article has been accepted for publication in Operations Research by INFORMS.
Publisher Keywords: tochastic sum; probability distribution; matrix exponential and column vector differentiation; Pearson curve fit; pricing
Subjects: H Social Sciences > HB Economic Theory
H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management
Q Science > QA Mathematics
Departments: Bayes Business School > Actuarial Science & Insurance
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