Abstract
We review important results of stochastic calculus. We introduce a Brownian motion, a random measure and a compensated random measure. Examples of Lévy processes, step processes and their jump measures are given. We investigate stochastic integrals with respect to Brownian motion and compensated random measures and we recall their properties. We discuss the weak property of predictable representation for local martingales. Equivalent probability measures are defined, and Girsanov’s theorem for Brownian motion and random measures is stated. We give differentiation rules of the Malliavin calculus.
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Delong, Ł. (2013). Stochastic Calculus. In: Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications. EAA Series. Springer, London. https://doi.org/10.1007/978-1-4471-5331-3_2
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DOI: https://doi.org/10.1007/978-1-4471-5331-3_2
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5330-6
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