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Elements of Stochastic Calculus

In: Capital Market Finance

Author

Listed:
  • Patrice Poncet

    (ESSEC Business School)

  • Roland Portait

    (ESSEC Business School)

Abstract

This chapter presents the elements of calculus relevant to Itô processes, which are extensively used in the theory and techniques of modern finance. It focuses on computational tools as these are needed to understand many chapters. More detailed mathematical exposition is to be found in footnotes and in the following chapter. After providing several general definitions about stochastic processes of various types (Sect. 18.1), we examine Brownian motions (Sect. 18.2), one-dimensional Itô and diffusion processes (Sect. 18.3), properties of functions of stochastic processes and the rules of Itô differential and integral calculus (Sects. 18.4 and 18.5) and, briefly, Poisson-like processes that present jumps occurring at random times (Sect. 18.6).

Suggested Citation

  • Patrice Poncet & Roland Portait, 2022. "Elements of Stochastic Calculus," Springer Texts in Business and Economics, in: Capital Market Finance, chapter 18, pages 765-796, Springer.
    • Handle: RePEc:spr:sptchp:978-3-030-84600-8_18
    DOI: 10.1007/978-3-030-84600-8_18
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