An Introduction to Stochastic Calculus
Stochastic calculus is a branch of mathematics that operates on stochastic processes and is utilized in various fields, such as finance, economics, and other areas involving random phenomena.
Unlike classical calculus, which deals with deterministic functions, stochastic calculus incorporates randomness, providing a framework to model the evolution of random variables over time. A foundational concept within stochastic calculus is the Wiener process or Brownian motion. This process is critical in modeling fluctuating stock prices in financial markets.
Applications
- Black-Scholes option pricing model
- Portfolio optimization
- Risk management
- Various forms of stochastic differential equations (SDEs)
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