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# All Questions

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### Smoothness of an optimal control problem for a point process

Let $\theta \in \{0,1\}$ be an unknown state of the world. Let $P_0 := Prob(\theta = 1)$ at time $0$. Let $G_t$ and $B_t$ be two Poisson processes with stochastic intensity $\lambda_g e_t \theta$ ...
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### Optimal control of SDEs

I've set up a system of stochastic differential equations that I'd like to control. I'm new to optimal control theory and SDEs (and, admittedly, weak on PDEs), so I'm not certain if I've set this up ...
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We know how to find the stochastic differential equation (Hamilton-Jacobi-Bellman equation, HJB) of the control problem where a process $X_t$ is controlled up until it is stopped at a stopping time $\... 1answer 532 views ### Supremum in a Markov chain model A Markov chain$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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