Introduction to Mathematical Finance - 2018

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Marc, 14.08.2018, 08:00-08:30

The exam took place at the table (on paper), Prof. Schweizer was sitting to your left and the assistant to your right.

• First, he asked me what I know about hedging duality? I stated Theorem II.7.2. Then he asked me if the infimum in 3), i.e. \( \pi_s (H) := \inf \Gamma (H) \), is really attained or how one could check this. Afterwards, I had to prove the direction "\( \Leftarrow \)" in 1), that would be the interesting direction he said.

• Next, he wanted to hear what I know about Mean Variance Hedging. I gave him the definition of that as in Exercise 10.1. He then wanted to know how one could check existence of such a minimiser for that problem (this task was not done in the exercises he then told me). At this point, I didn't really know how to argue for that, but he tried to give me some hints how to get it. He helped and asked what I can say about the set \( G_T(\Theta) \cap L^2 \) over which we should minimise. One should have argued that this set was closed in \( L^0 \) by arguing that \( G_T(\Theta) \) was closed in \( L^0 \) (and \( L^2 \) of course also, if I remember that correctly) and so on. He obviously wanted to hear Proposition II.3.4 and the idea of that proof, which I couldn't remember unfortunately.

• After that, he wanted to hear Theorem II.3.1. before Dalang-Morton-Willinger and from this one he wanted me to explain how we checked that 4) implies 5).

In general, Prof. Schweizer stays calm and tries to give you hints if you don't get something immediately. But in my opinion he insists way too much on solving his given task instead of changing to another question you could probably answer better.