Syllabus for MTH 9862              file:///home/elena/teaching/fincal/syllabus.html
       Tentative Syllabus for MTH 9862: Stochastic
       Finance
       Instructor: Elena Kosygina
       Office: VC 6-245
       Phone: (646) 312-4167
       Email: elena.kosygina@baruch.cuny.edu
       Textbook: None required. Recommended: Steven Shreve, Stochastic Calculus
       for Finance II: Continuous-Time Models, Springer, ISBN: 0-387-40101-6.
       Tentative syllabus mostly follows Shreve's book (Chapters 4-10).
        1. Brownian Motion
             Review of basic properties and related matringales
             Quadratic Variation
        2. Stochastic Calculus
             Ito's Integral
             Ito's Formula in one dimension
             Black-Scholes-Merton equation
             Multivariable Stochastic Calculus
             Brownian Bridge (time permitting)
        3. Risk-Neutral Pricing
             Risk-Neutral Measure and Girsanov's Theorem in one dimension
             Martingale Representation Theorem and its application to hedging
             Fundamental Theorems of Asset Pricing
             Dividend-Paying Stocks (time permitting)
             Forwards and Futures (time permitting)
        4. Connections with Partial Differential Equations
             Stochastic Differential Equations
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  Syllabus for MTH 9862              file:///home/elena/teaching/fincal/syllabus.html
             Partial Differential Equations
             Feynman-Kac formula
        5. Exotic Options
             Maximum of Brownian Motion with Drift
             Knock-out Barrier Options
             Lookback Options (time permitting)
             Asian Options
        6. American Derivative Securities
             Perpetual Americal Put
             Finite-Expiration American Put
        7. Numeraires. Forward Measures.
        8. Term Structure Models
             Affine Yield Models
             Heath-Jarrow-Morton Model
             Forward LIBOR Model
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