Random Variables: Linearity and Order

Pablo Koch-Medina and Cosimo Munari
Additional contact information
Pablo Koch-Medina: University of Zurich, Department of Banking and Finance
Cosimo Munari: University of Zurich, Department of Banking and Finance

Chapter 1 in Market-Consistent Prices, 2020, pp 1-24 from Springer

Abstract: Abstract The topic of this book requires us to deal with quantities, such as future payments or prices, whose value is not known in advance. To this effect, we first need to develop the basic mathematics to model uncertainty. This chapter is devoted to introducing the notion of a sample space, corresponding to the set of possible outcomes of a situation of uncertainty, and of a random variable, a quantity that is contingent on those outcomes. We equip the set of random variables with the structure of an ordered vector space. This structure, in particular, allows us to treat the notion of convexity which pervades much of mathematical finance. Although the main topic of our book is mathematical finance, much of the theory of random variables originated with the study of games of chance, a fact that is reflected in most of the examples with which we illustrate the basic theory.

Date: 2020
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:sprchp:978-3-030-39724-1_1

Ordering information: This item can be ordered from
http://www.springer.com/9783030397241

DOI: 10.1007/978-3-030-39724-1_1

Access Statistics for this chapter

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