Handbook

Appreciate the modern approach to evaluation of uncertain future payoffs;

Describe the concepts of arbitrage and fair games and their relevance to finance and insurance;

Understand conditional expectation, martingales, and stopping times, as well as the Optional Stopping Theorem;

Interpret models of random processes such as random walk, Brownian motion and diffusion, and stochastic differential equations;

Use Ito's formula and basic stochastic calculus to solve some stochastic differential equations;

Apply the Fundamental theorems of asset pricing to the Binomial and Black-Scholes models, as well as models for bonds and options on bonds;

Formulate discrete time Risk Model in Insurance and use the Optional Stopping Theorem to control probabilities of ruin;

Simulate stochastic processes and solutions of stochastic differential equations, and obtain prices by simulations.