On the new properties of conditional expectations with applications in finance
The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a random variable as a function of another random variable. Thi...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
06.10.2022
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2210.02859 |
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| Summary: | The concept of conditional expectation is important in applications of
probability and statistics in many areas such as reliability engineering,
economy, finance, and actuarial sciences due to its property of being the best
predictor of a random variable as a function of another random variable. This
concept also is essential in the martingale theory and theory of Markov
processes. Even though, there has been studied and published many interesting
properties of conditional expectations with respect to a sigma-algebra
generated by a random variable it remains an attractive subject having
interesting applications in many fields. In this paper, we present some new
properties of the conditional expectation of a random variable given another
random variable and describe useful applications in problems of per-share-price
of stock markets. The copula and dependence properties of conditional
expectations as random variables are also studied. We present also some new
equalities having interesting applications and results in martingale theory and
Markov processes. Keywords: Conditional expectation, sigma algebra, per-share
price, order statistics, prediction Conflicts of interest statement: We declare
that have no conflicts of interest. |
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| DOI: | 10.48550/arxiv.2210.02859 |