A gentle introduction to mathematical finance: The mathematical theory of arbitrage, pricing and hedging of derivative securities in a discrete, elementary setting.

Option, Futures, and other derivative securities The one-period binomial model The multiperiod Cox-Ross-Rubinstein binomial model American Options, optimal stopping, and the Bellman principle Exotic options for random walks Rubinstein's implied binomial trees General theory in a discrete setting: The Harrison-Pliska fundamental theorem of asset pricing Incomplete markets, Superhedging, Utility maximization Discrete term structure models

Stanley R. Pliska: "Introduction to Mathematical Finance: Discrete Time Models" Steven E. Shreve: "Stochastic Calculus Models for Finance I: The Binomial Asset Pricing Model" Hans Föllmer and Alexander Schied: "Stochastic finance. An introduction in discrete time." John Hull: "Options, Futures, and Other Derivatives"