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

The one-period model (Arbitrage, risk neutral measure, pricing, complete markets, optimal portfolios) The multiperiod model (self-financing portfolios, duality, Dalang/Morton/Willinger theorem) Capital Asset Pricing Model (CAPM) The Binomial Model, Cox-Ross-Rubinstein Model, distribution of the maximum Markov Models Taking limits in the Binomial Model, Black-Scholes Model American Options, Snell envelope, Doop decomposition Optimal portfolios

Lecture notes for this course are available. http://reinhold.kainhofer.com/Lehre/07S_VU_DiskreteModelle/Skriptum_DiskreteModelle.pdf Stanley R. Pliska: "Introduction to Mathematical Finance: Discrete Time Models" Daniel Lamberton, Bernard Lapeyre: "Stochastic Calculus Applied to Finance"0 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"