All Questions
8 questions
2
votes
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207
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Elliptic PDEs in BSDEs and in optimal control
This soft/reference question is related to this MO post of a similar nature.
What are some examples of elliptic PDEs appearing in control and BSDEs?
- 6,155
1
vote
0
answers
59
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Representation of optimal controls as diffusions
In reading this post I couldn't help but wonder the following question:
Let $\sigma>0$ and suppose, as in the motivational post, we are given a stochastic optimal control problem:
$$
\begin{...
- 63.9k
4
votes
1
answer
610
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Stochastic differential equation associated with an optimal control problem
We know how to find the stochastic differential equation (Hamilton-Jacobi-Bellman equation, HJB) of the control problem where a process $X_t$ is controlled up until it is stopped at a stopping time $\...
- 1,675
1
vote
0
answers
79
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Stochastic Control with Stochastic Cost-functional
Is there any literature dealing with a stochastic control problem whose cost-functional $J_t$ is stochastic also?
That is, let $X_t^u$ is the solution to a controlled SDE
$$
dX_t = \mu(t,u_t,X_t^u)dt ...
- 5,405
1
vote
2
answers
2k
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Deriving the HJB equation for exponential utility
I would like to derive the HJB equation for the following stochastic optimal control problem:
$ \Phi(t,x)=\sup_{h} E \left[\exp \left\{\gamma \int_t^T g(X_s,h(s);\gamma)\ ds \right\} \right]$
where ...
- 6,045
5
votes
0
answers
275
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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 ...
- 427
0
votes
0
answers
77
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Law of motion when initial condition is perturbed
We know how to find the law of motion (Ito process) of the value function:
$$V_t(x)=E\Big{[}\int^{T}_te^{-r (s-t)}f(s,X_s)ds+e^{-r (T-t)}g(T, X_{T})|\mathcal{F}_t\Big{]}$$
such that
$$dX_t=\mu(t,X_t)...
- 1,533
3
votes
1
answer
299
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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 ...
- 41.1k