Abstract: We consider a control problem for multidimensional martingales in a radially symmetric environment. We provide an explicit construction of the value function by reducing the problem to a one-dimensional switching problem with two behaviour regimes. Under mild conditions on the cost function, we can see that the optimal martingale is Markovian. For a particular class of cost functions, however, we conjecture that any Markov martingale is suboptimal. In support of this conjecture, we prove that an SDE describing the optimal behaviour does not admit a strong solution. In this case, we also require results on Brownian filtrations in order to find the value function. This is based on joint work with Alexander Cox.
Optimal control of martingales in a radially symmetric environment
29.04.2021 16:30 - 17:30
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