2
votes
1answer
134 views

Upper bound concerning Snell envelope

Consider, on a filtred probability space $ \left (\Omega, \mathcal F, \mathbb F , \mathbb P \right )$ where $ \mathbb F = \left(\mathcal F_ t \right )_ {t\geq 0}$ is filtration satisfying the usuual ...
3
votes
0answers
146 views

stochastic control / geometric mean

Consider the following problem: Given $\Omega$ and $U$ two symmetric definite positive matrices, choose a matrix $K$ to minimize the expectation $x' \Omega x + x'K'UKx$ when $x$ follows the invariant ...
0
votes
0answers
194 views

Stochastic Optimal Control - Maximizing convex terminal costs

The theory of stochastic optimal control deals with the following problem: Find $\quad\sup\limits_{u} \; \mathrm E[g(X^{(u,x)}_T)]$ where $X^{(u,x)}_t$ solves the following controlled SDE: ...
4
votes
0answers
457 views

Dynamic programming principle (DPP)

In stochastic control problem, one shall use the measurable selection theorem to prove DPP. It was discussed in discrete time case in [Bertsekas and Shreve 1978]. Is there unified framework in ...