Financial Mathematics
Explore time and risk models; arbitrage and discrete pricing; continuous models and limits. Concepts and connections are available independently of video coverage.
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Brownian motion
Brownian motion has continuous paths and independent Gaussian increments with variance equal to elapsed time.
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Expectation
Expectation is a probability-weighted average when defined; not every random variable has a finite expectation.
Geometric Brownian motion
A multiplicative stochastic differential model keeps positive initial asset prices positive.
Poisson processes
A homogeneous Poisson process counts events with stationary independent increments at a constant rate.
Renewal processes
Independent identically distributed waiting times generate repeated renewal events.
Time value of money
Discounting compares amounts at different dates under a specified rate model.
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- Poisson processes · Related · Map context
- Renewal processes · Related · Map context
- Expectation · Related · Map context
- Time value of money · Related · Map context
- Geometric Brownian motion · Related · Map context
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Stochastic Processes
Explore processes and dependence; counting and continuous paths; information and stochastic calculus. Concepts and connections are available independently of video coverage.