medium · Quantitative Finance

Given a filtered probability space (Ω, mathcalF, mathcalF_t, mathbbP) where the filtration is generated by a standard Brownian motion W_t, what does the Martingale Representation Theorem (MRT) imply about a local martingale M_t?

1. The process M_t is always a martingale under any equivalent measure mathbbQ.
2. The martingale M_t can be represented as M_t = M_0 + int_0^t H_s ds.
3. The integrand H_t in the representation M_t = M_0 + int_0^t H_s dW_s must be a deterministic function of time.
4. There exists a unique predictable process H_t such that M_t = M_0 + int_0^t H_s dW_s.

Sign up free to see the explanation and track your rank →