Questions on stochastic programming, a method for modeling optimization problems that involve uncertainty.
Questions tagged [stochastic-programming]
21 questions
3
votes
0 answers
Why is it valid to derive a stochastic Euler equation?
Suppose we are given a stochastic dynamic programming problem.
$$\max E\sum_{t=0}^T F(t,X_t, X_{t+1}(X_t,V_{t}),V_{t})$$
Where $V_t$ is a random variable, correlated possibly with $V_{t-1}$. In this problem, we assume that the "optimizer" can…
user56834
- 12,323
2
votes
1 answer
Stochastic dynamic programming
I am making some homework exercises at the moment and I was wondering if what I did in the following exercise was correct.
PROBLEM
Solve $E(\sum_{k=0}^{N-1}(1-u_k)X_k + X_N) \rightarrow \max$, where $N\in\mathbb{N}$ is fixed $u_k$ are control…
Nedellyzer
- 1,184
2
votes
0 answers
Kalman Filtering the Vasicek Model, are there different Kalman Filters for the same application?
While studying parameter estimation in affine term structure models, I stumbeled across two papers.
Affine Term-Structure Models: Theory and Implementation by David Bolder…
reni_schmitt
- 21
2
votes
0 answers
Nested form of a stochastic optimization problem
I'm working on an energy load scheduler. Basically, I'm trying to find an algorithm that turns on deferrable load (think of a dishwasher or a washing machine) when there is a surplus of solar energy. The idea is to turn the deferrable appliances in…
Armen Firman
- 21
2
votes
0 answers
Solutions for “Stochastic Programming: Modeling Decision Problems Under Uncertainty".
I am currently reading Stochastic Programming: Modeling Decision Problems Under Uncertainty by Willem K. Klein Haneveld, Maarten H. van der Vlerk, and Ward Romeijnders (the 2020 Springer edition), and I am interested in solving the…
sebejok535
- 21
2
votes
1 answer
Chance constrained stochastic programming
A stochastic programming optimizes the expectation of a cost function with respect to values.
\begin{cases}
{\boldsymbol x}=\text{argmin}~ E(f({\boldsymbol x}))\\
{\boldsymbol g}({\boldsymbol x})<{\boldsymbol 0}
\end{cases}
where $E$ refers to…
Adams
- 145
- 1
- 7
2
votes
0 answers
Stochastic optimization vs stochastic programming
How should I think about the differences between stochastic optimization (SO) and stochastic programming (SP)? From Wikipedia, it seems that SO is a framework that uses randomness to solve a pre-existing optimization problem whereas SP uses…
jjjjjj
- 2,779
2
votes
1 answer
Expectation of piece-wise objective function
I recently started reading ''Lectures On Stochastic Programming'' by Alexander Shapiro, Darinka Dentcheva & Andrzej Ruszczyński. On the introduction they adress the News Vendor Problem:
Suppose that a company has to decide about order quantity $x$…
1
vote
0 answers
Stochastic Portfolio Optimization with Recourse
I am given the following problem from a tutorial in my course:
(Portfolio Optimization with Recourse). You have £10,000 to invest (without short
selling) in a portfolio composed of eight leading stock market indices (think of investing in a market…
tealing123
- 321
1
vote
1 answer
Translation equivariance of AV@R (average value at risk), proof
I am trying to prove that the average value at risk is translation equivariant:
$$AV@R_\alpha[Z+\tau] = AV@R_\alpha[Z] + \tau$$
where
$$AV@R_\alpha[Z] := \inf_{t\in \mathbb{R}} \{t+\alpha^{-1} \mathbb{E}[(Z-t)_+] \}.$$
I started by plugging in the…
MDescamps
- 171
1
vote
1 answer
Optimality solutions of stochastic linear program
Given the random LP: $K(x,\epsilon) = min_{a=(a_1,a_2)}\ a_1(w) + a_2(w)$ such that
$$\ a_1(w) - a_2(w) = x-\epsilon$$ and $$a_1(w), a_2(w), x\geq 0,$$ where $\epsilon\sim U(0,1)$ and $w$ is the outcome of random variable $\epsilon$. Assume…
ghjk
- 2,937
1
vote
0 answers
Stochastic Dynamic Programming: Deriving the Steady-State for a Lottery
This question was originally posted here, but as the Math.SE community is more active I provide an extended version of the post here.
I am working through the basic examples of the stochastic optimization models in the book by McCandless (2008): The…
1
vote
0 answers
What is the role of the recourse variable in stochastic programming?
What is the role of recourse variable in stochastic programming?
I often see two-stage stochastic programming problems with recourse, written as follows:
Stage 1
\begin{equation}
\begin{array}{rrclcl}
\displaystyle \min_{x} \,\,\,{c^T x}…
makansij
- 1,643
1
vote
1 answer
Binary Stochastic Programming with Independent or Positively Correlated Co-efficients
A manufacturer can select a maximum of $N$ stores to fulfill orders
from a total of $M$ stores who are looking for inventory, $N\le M$.
The case when $N\geq M$ is trivially solved when all stores have
positive demand.
When a store is selected, it…
texmex
- 842
0
votes
0 answers
Delay in timetabling with supplements and exponentially distributed disturbances
I am looking at the following problem in operations research:
Suppose that a train is operated over two identical consecutive trips, where on each trip the train incurs an exponentially distributed disturbance with average $1/\lambda$. In order to…
Caliondo
- 11