Introduction to Mathematical Finance - 2019
From Math Wiki
09.08.2019 10:00-10:30
Topics: Def. Arbitrage, 1. FTAP (state + proof "easy" direction (i.e. exist EMM)), Def. Complete, 2. FTAP , Properties Utility Fuction (No consumption), How do you compare H_1 and H_2 with U?, compare E[H] and H with U (concavity), Proposition 4.21 with Proof (i.e. existence of optimal solution in complete market) and some other things i can't remember. They are really friendly and help you if you are confused.
Skander, 09.08.2019 13:00-13:30
- 1st FTAP statement
- 2nd FTAP statement
- Definition of Arbitrage in finite discrete time (Chap 2)
- Attainable payoff pricing statement (buyer's price=seller's price=sup over Equivalent Martingale Measures of expected value of payoff)
- Example of EMM for T=1, X0=1, X1=Y^2 where Y is standard Gaussian, F0 P-trivial, F1 generated by X1
- Characterisation of attainability with proof ideas (the completeness equivalence theorem)
- Definition Utility function and its assumptions
- Example of Utility comparison for H1=H, H2=E[H] (using concavity of U)
- Complete market solution to utility maximisation with proof
- Optional Decomposition Theorem statement
Prof. Larsson and Bálint seemed to be in a good mood and you get actually useful hints if you are stuck somewhere. It was very pleasant.
