Thesiss

Let Ω be the Fraïssé limit of a class of relational structures. We seek to answer the following semigroup theoretic question about Ω. What are the group H-classes, i.e. the maximal subgroups, of End(Ω)? Fraïssé limits for which we answer this question include the random graph R,…

The initial public offering (IPO) underpricing phenomenon has frequently been noticed and generally is accepted as a puzzle in financial economics. Some of the new theories, such as behavioural finance, take the underpricing puzzle as one important form of evidence. However, som…

In this dissertation, problems in stochastic analysis and control are investigated, which include mathematical finance, online learning, and mean field game. For math- ematical finance, 1) a martingale optimal transport problem with bounded volatility is studied, which allows to…