Stochastic analysis in financial and actuarial mathematics

Additional Info

  • ECTS credits: 7
  • University: Vienna University of Technology
  • Semester: 3
  • Objectives:

     

    Introduction to stochastic analysis as needed for continuous-time financial and actuarial mathematics.

  • Topics:

     

    Definition and properties of multi-dimensional normal distribution, definition and elementary properties of Brownian motion, existence and Hölder continuity of Brownian motion using the Kolmogorov-Chentsov continuity criterion, filtrations, stopping times, progressive measurability, path properties, martingales, uniform integrability, Vitali's convergence theorem, sub- and supermartingales, maximum inequality, Doob's inequality for p-integrable submartingales, Doob's optional sampling theorem with applications, local martingales and examples, integration of predictable step processes, p-variation of functions, quadratic variation and covariation process of continuous local martingales, Kunita-Watanabe inequality, stochastic integration for continuous local martingales and generalization for continuous semimartingales.

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