*The Mathematical Framework of Financial Markets Theory

Patrice Poncet () and Roland Portait ()
Additional contact information
Patrice Poncet: ESSEC Business School
Roland Portait: ESSEC Business School

Chapter 19 in Capital Market Finance, 2022, pp 797-846 from Springer

Abstract: 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.

Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sptchp:978-3-030-84600-8_19

Ordering information: This item can be ordered from
http://www.springer.com/9783030846008

DOI: 10.1007/978-3-030-84600-8_19

Access Statistics for this chapter

More chapters in Springer Texts in Business and Economics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().