Abstract
In this chapter we introduce the elements of stochastic integration theory that are necessary to treat some financial models in continuous time. In Paragraph 3.4 we gave grounds for the interest in the study of the limit of a Riemann-Stieltjes sum of the form
as the refinement parameter of the partition {t0, . . . , t N } tends to zero. In (4.1) W is a real Brownian motion that represents a risky asset and u is an adapted process that represents an investment strategy: if the strategy is self-financing, the limit of the sum in (4.1) is equal to the value of the investment.
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© 2011 Springer-Verlag Italia
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Pascucci, A. (2011). Brownian integration. In: PDE and Martingale Methods in Option Pricing. Bocconi & Springer Series. Springer, Milano. https://doi.org/10.1007/978-88-470-1781-8_4
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DOI: https://doi.org/10.1007/978-88-470-1781-8_4
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-1780-1
Online ISBN: 978-88-470-1781-8
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