IAM743 SPECIAL TOPICS: MALLIAVIN CALCULUS AND ITS APPLICATIONS
|METU Credit (Theoretical-Laboratory hours/week):||3(3-0)|
|Department:||Institute Of Applied Mathematics|
|Language of Instruction:||English|
|Level of Study:||Graduate|
|Offered Semester:||Fall or Spring Semesters.|
Course ContentImportant markets such as commodities or credit derivatives are essentially incomplete. The recent financial crisis has increased even more the importance of pricing and hedging in incomplete markets. Therefore these lectures concentrate on advanced methods of stochastic finance required in the context of incomplete markets. We will consider both, process in discrete and continuous time.
The content of the course covers in particular the following topics: market efficiency, market incompleteness; perfect hedges; equivalent martingale measures; attainable payoffs; asset management; contingent claims; replicating portfolio; dynamical arbitrage theory; arbitrage-free pricing; geometric characterization of arbitrage; von Neumann representation; robust Savage representation; expected utility; fair value; certainty equivalent; risk premium; risk aversion; equilibrium pricing; relative entropy; convex risk measures; robust representation; coherent risk measures; VAR; average VAR; upper/lower hedging prices; superhedging duality; risk indifference pricing; HJB equations; dynamical programming.