STOCHASTIC CALCULUS.

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Course Code: 
MTM 7202
Course Credit Units: 
2
Semester: 
Semester 2
Year of Study: 
Year 1
Undergraduate or Graduate Level: 
Graduate Level
Course Description & Objectives: 

Stochastic calculus can be loosely described as a field of mathematics that is concerned with infinitesimal calculus on non-differentiable functions.  This course aims at providing a rigorous treatment to stochastic calculus with some of its applications in Finance, Engineering and Science. It will bridge the gap of an increasing demand for tools and methods of stochastic calculus in various disciplines. Most popular applications of stochastic calculus are: pricing and hedging of financial derivatives, filtering and control theory, in studying the effects of random excitations on various physical phenomena, modelling the effects of stochastic variability in reproduction and environment on populations, stochastic models in insurance mathematics.

Learning Outcomes: 

At the end of this course the student should be able to

  • use Ito calculus on Stochastic Differential Equations (SDEs)
  • solve and interpret classes of stochastic differential equations (SDEs)
  • state and prove Girsanov theorem
  • construct and justify numerical schemes to simulate SDEs
  • apply SDEs to solve some problems in various applications
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STOCHASTIC CALCULUS
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