We will have a research seminar this semester on forking, broadly construed, particularly in the setting of unstable first-order theories. Graduate students are particularly encouraged to attend. We will discuss Dobrowolski, Kim and Ramsey's question of whether every NSOP_1 theory has the existence axiom, and the recent example, answering this question, of an NSOP_1 theory without the existence axiom. Continuing our discussion from last time about questions for possible future collaboration, we will conclude this seminar by giving some open problems on the existence axiom.

It is well known that asset returns usually do not follow a normal distribution, rather, they have long and fat tails. This paper focuses on the quantile portfolio methodology, which considers the whole distribution of asset returns and employs expected loss as a risk measurement. In particular, we explore statistical properties of tau risk and propose related theories of quantile portfolio optimization. We also introduce portfolio performance terms for the quantile portfolio framework.