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*The Mathematical Framework of Financial Markets Theory

In: Capital Market Finance

Author

Listed:
  • Patrice Poncet

    (ESSEC Business School)

  • Roland Portait

    (ESSEC Business School)

Abstract

The modern theory of financial markets provides precise answers to issues such as probability changes, the notion of risk-neutral world, changes in numeraire, and market completeness. It is grounded on the theory of probability and stochastic processes and provides a coherent analytical framework. The general framework is given in Sect. 1. A more constrained framework in which asset prices obey Itô processes is presented in Sect. 2. The risk-neutral world and transforming prices into martingales are described in Sect. 3. Changing the probability measure is studied in Sect. 4 and changing numeraires associated with martingale probabilities in Sect. 5. Section 6 is devoted to the logarithmic portfolio which is the numeraire that leads to martingale prices under the true probability. Section 7 discusses incomplete markets.

Suggested Citation

  • Patrice Poncet & Roland Portait, 2022. "*The Mathematical Framework of Financial Markets Theory," Springer Texts in Business and Economics, in: Capital Market Finance, chapter 19, pages 797-846, Springer.
    • Handle: RePEc:spr:sptchp:978-3-030-84600-8_19
    DOI: 10.1007/978-3-030-84600-8_19
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