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Financial Mathematics by Roman N. Makarov, Giuseppe Campolieti

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Chapter 6

Introduction to Discrete-Time Stochastic Calculus

The term stochastic means random. Because it is usually used together with the term process, it makes people think of something that changes in a random way over time. The term calculus refers to ways to calculate things or find objects that can be calculated (like derivatives in the differential calculus). Stochastic Calculus is the study of stochastic processes through a collection of special methods such as stochastic differential equations and stochastic integrals used to find probability distributions and to compute quantitative characteristics. Many fundamental concepts of stochastic calculus like filtration, conditioning, martingale, and stopping time are easy to introduce in ...

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