Measure, probability, and mathematical finance : a problem-oriented approach / Guojun Gan, Chaoqun Ma, Hong Xie.

Includes bibliographical references (p.687-702) and index.

Preface -- Measure theory -- Sets and sequences -- Measures -- Extension of measures -- Lebesgue Stieltjee measures -- Measurable functions -- Lebesgue integration -- The Radon Nikodym theorem -- LP spaces -- Convergence -- Product measures -- Probability theory -- Events and random variables -- Independence -- Expectation -- Conditional expectation -- Inequalities -- Law of large numbers -- Characteristic functions -- Discrete distributions -- Continuous distributions -- Central limit theorems -- Stochastic processes -- Martingales -- Stopping times -- Martingale inequalities -- Martingale convergence theorems -- Random walks -- Poisson processes -- Brownian motions -- Markov processes -- Levy processes -- Stochastic calculus -- The wiener integral -- The it "o" integral -- Extension of it "o" integrals -- Martingale stochastic integrals -- The it o's formula -- Martingale representation theorem -- Change of measure -- Stochastic differential equations -- Libor market models -- Diffusions -- The Feyn Mankac formula -- Stochastic financial models -- Discretetime models -- Blackscholes -- Pathdependent options -- American options -- Instantaneous forward rate models.