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

Author

Listed:
  • Milan Kumar Das

    (Institute of Statistical Science, Academia Sinica, Taiwan (ROC))

  • Henghsiu Tsai

    (Institute of Statistical Science, Academia Sinica, Taiwan (ROC))

  • Ioannis Kyriakou

    (Faculty of Actuarial Science & Insurance, Bayes Business School, City, University of London, London EC1Y 8TZ, United Kingdom)

  • Gianluca Fusai

    (Dipartimento di Studi per l’Economia e l’Impresa, Università del Piemonte Orientale, 28100 Novara, Italy; Faculty of Finance, Bayes Business School, City, University of London, London EC1Y 8TZ, United Kingdom)

Abstract

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.

Suggested Citation

  • Milan Kumar Das & Henghsiu Tsai & Ioannis Kyriakou & Gianluca Fusai, 2022. "Technical Note—On Matrix Exponential Differentiation with Application to Weighted Sum Distributions," Operations Research, INFORMS, vol. 70(4), pages 1984-1995, July.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:4:p:1984-1995
    DOI: 10.1287/opre.2021.2257
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