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Conditioning on an irrelevant variable in a martingale control problem
Suppose I have two independent Brownian motions $B^1_t, B^2_t$ and $\mathbb F_t$ be the natural filtration generated by them. Let $T > 0$ be a fixed finite number. Let $q_t$ be a $[-1,1]$ valued $\...
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Supremum in a Markov chain model
A Markov chain $X$ with finite state space $\{1,2,\cdots,N\}$ is defined on a probability space $(\Omega, P, \mathcal{F})$ equiped with filtration $\{\mathcal{F}_t\}$. And we assume that we can reach ...
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