Abstract
The chapter introduces the multi-period dynamic securities market model, an extension of the two-period model, which served as the main framework in Part I of the book. It states a multi-period version of the no-arbitrage hypothesis and discusses the concepts of market scenarios (histories), contingent portfolios, trading strategies, self-financing trading strategies, contingent claims and derivative securities. It presents one of the highlights of Mathematical Finance: the no-arbitrage pricing principle for contingent claims. The chapter concludes with defining the net present value (NPV) of a trading strategy and establishing an equivalent version of the no-arbitrage hypothesis stated in terms of the NPV.
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Notes
- 1.
The terms “probability measure”, “probability distribution”, or simply “probability” are used interchangeably.
- 2.
In the mean-variance portfolio theory, we characterized portfolio positions, basically, in terms of the sums of money invested in one asset or another. Here, it is more convenient to deal with units of assets.
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Evstigneev, I.V., Hens, T., Schenk-Hoppé, K.R. (2015). Dynamic Securities Market Model. In: Mathematical Financial Economics. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-16571-4_11
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DOI: https://doi.org/10.1007/978-3-319-16571-4_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16570-7
Online ISBN: 978-3-319-16571-4
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