4
votes
0answers
104 views

compactness of a probability set

I have a question about the compactness of a set of martingale measures. Let $\Omega=\mathcal{C}[0,1]$ be the space of continuous functions on $[0,1]$ and $\mathcal{M}_{\Omega}$ be the family of ...
8
votes
3answers
716 views

Compactness of the set of densities of equivalent martingale measures

Consider an incomplete market $(\Omega,\mathcal F,\mathbb P)$ driven by a semimartingale $S=(S_t)_{t\in[0,T]}$. Under the no free lunch under vanishing risk (NFLVR) assumption, the set $\mathcal ...
5
votes
1answer
322 views

Stieltjes integrals of predictable processes

I am looking for a direct proof of the fact that, roughly speaking, if $S=S_0+A+M$ is an $L^2$ semimartingale, and $M$ (the martingale part) has the martingale representation property, then for any ...