medium · Quantitative Finance stochastic
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?
- The process M_t is always a martingale under any equivalent measure mathbbQ.
- The martingale M_t can be represented as M_t = M_0 + int_0^t H_s ds.
- 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.
- There exists a unique predictable process H_t such that M_t = M_0 + int_0^t H_s dW_s.
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