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What are prerequisite for stochastic calculus?
The official prerequisites are an introductory probability course (Math 309/Stat 311/Math 431/Math 531) and a course in linear algebra or intro to proofs (Math 320/340/341/375/421). It is important to have a good knowledge of undergraduate probability.
Is stochastic calculus useful?
An important application of stochastic calculus is in mathematical finance, in which asset prices are often assumed to follow stochastic differential equations. In the Black–Scholes model, prices are assumed to follow geometric Brownian motion.
Is stochastic calculus still used in finance?
Stochastic calculus is widely used in quantitative finance as a means of modelling random asset prices. In quantitative finance, the theory is known as Ito Calculus. The main use of stochastic calculus in finance is through modeling the random motion of an asset price in the Black-Scholes model.
Why do we study stochastic calculus?
Stochastic calculus is the mathematics used for modeling financial options. It is used to model investor behavior and asset pricing. It has also found applications in fields such as control theory and mathematical biology.
How to start learning stochastic calculus?
To gain a working knowledge of stochastic calculus, you don’t need all that functional analysis/ measure theory. What you need is a good foundation in probability, an understanding of stochastic processes (basic ones [markov chains, queues, renewals], what they are, what they look like, applications, markov properties),…
What are the prerequisites for studying stochastic analysis?
What you need is a good foundation in probability, an understanding of stochastic processes (basic ones [markov chains, queues, renewals], what they are, what they look like, applications, markov properties), calculus 2-3 (Taylor expansions are the key) and basic differential equations. Some people here are trying to scare you away.
Is it possible to apply stochastic calculus without knowing mean square limit?
It is certainly possible to apply stochastic calculus and gain an intuitive understanding of what’s going on without knowing the details of a mean square limit or how to prove a function is square integrable in Lp space. After all, it is a tool that first came into being for thermodynamic processes.