Random Variables: Information and Measurability

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

Chapter 9 in Market-Consistent Prices, 2020, pp 159-173 from Springer

Abstract: Abstract With this chapter we start collecting the necessary mathematical tools to model multi-period financial markets. The objective is to introduce partitions of the sample space as a way of modeling the granularity of the information we may obtain about the outcome of a random experiment. The highest granularity corresponds to full information and the lowest to no information. Intermediate granularity levels correspond to partial information. A key concept related to a partition is that of a random variable that is measurable with respect to it, i.e., a random variable whose value can be determined after receiving the information in the granularity of the partition. Familiarity with these notions is indispensable for understanding the modelling of how information about the terminal state of the economy increases as time passes.

Date: 2020
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DOI: 10.1007/978-3-030-39724-1_9

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