Stochastic Calculus: Interest Rate Models

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Sub- and Supermartingales: Theory and Applications

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Linear Response and Complex Diffusivity

Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.

Stochastic Integration

Covers stochastic integration and exchange mobility for mathematics students.

Stochastic Processes: Brownian Motion

Explores Brownian motion, Langevin equations, and stochastic processes in physics.

White Noise Form of the Langevin Equation

Covers the white noise form of the Langevin equation and its applications.

Risk-neutral Valuation

Explores risk-neutral valuation for European derivatives, EMMs, trading strategies, and market securities in financial modeling.

Turbulent State Symmetries

Explores broken and emerging symmetries in turbulent states, discussing energy cascades, lack of scale invariance, and potential conformal invariance.

Asset Pricing: Dynamic Arbitrage Pricing & Black-Scholes Formula

Explores asset pricing theorems and the Black-Scholes formula derivation in discrete time economies.

Joint Quadratic Processes

Covers the concept of joint quadratic processes and their properties.

Doob's Decomposition Theorem

Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.