Tagged Questions
1
vote
0answers
79 views
pricing of heat rate-linked derivative [migrated]
It's a simplified model.
Suppose $U_t$ is a random variables subject to Lognormal($x_1$, $z_1^2$)distribution. $V_t$ is a random variables subject to Lognormal($x_2$, $z_2^2$)distribution. Suppose ...
0
votes
1answer
32 views
Optimize winnings in a money making game.
So, given a continuous random variable A (with some density and CDF function), and a value I choose V, what is the equation to determine the best value V to maximize my earnings given that I will be ...
1
vote
2answers
35 views
gradient descent optimal step size
Suppose a differentiable, convex function $F(x)$ exists. Then $b = a - \gamma\bigtriangledown F(a)$ imples that $F(b) <= F(a)$ given $\gamma$ is chosen properly. The goal is to find the optimal ...
2
votes
1answer
47 views
Optimal strategy puzzle
Play a game with an urn. $75$ blue balls. $25$ red balls. $1$ yellow ball. you get a dollar for every red and if you select the yellow you lose everything. what should be your strategy in the game. ...
0
votes
0answers
31 views
Facets of the convex hull as solution of an optimization problem?
Given $N$ points $x_1, x_2, ..., x_N \in \mathbb{R}^n$, consider their convex hull $$\mathcal{C} = \text{conv}( \{ x_1, ..., x_n \} ) = \bigcap_{j=1}^{J} \{ x \in \mathbb{R}^n : \ A_j x \leq b_j \} ...
0
votes
1answer
22 views
What is the optimal stopping point for an experiment when expecting unknown event
Assume we notice that stock prices are rising and we can deduce we are in a bubble. Assume we start at $w(0)=0$ worth at time $t=0$ and the value grows linearly with time $(w(t)=t)$. We know that ...
0
votes
2answers
61 views
Anyone saw this interesting function before?
Say $\theta\in\Re^n$ and $\theta_i\in(0,1)$ for all $i$. Define
$$
f(\theta) = \frac{1}{n}\sum_i^n\{(1-\theta_i)\log(1-\theta_i)+\theta_i\log\theta_i\}
$$
It is easy to see the minimizer of ...
2
votes
3answers
50 views
Packing radios into cartons - why is my solution wrong?
A manufacturer of car radios ships them to retailers in cartons of $n$ radios. The profit per radio is $\$59.50$, minus shipping cost of $\$25$ per carton, so the profit is $59.5n-25$ dollars per ...
-1
votes
1answer
77 views
Inverse transform sampling
I know the basic idea is to generate a random number from $U(0,1)$, find the inverse cumulative distribution function $F^{-1}$ and then take $x = F^{-1}(U)$. If you were plot a histogram of say 1000 ...
4
votes
1answer
140 views
Optimal Yahtzee (Dice roll) decisions: Probability and weighting choices
I'm a senior in computer science, and I have a hobby of taking on little projects that I find interesting. My current one is a Yahtzee optimal play solver. One would enter their current roll, and it ...
1
vote
0answers
31 views
Optimal distribution with moment conditions
Basically, I want to find a probability distribution which maximizes a convex objective function and satisfies two moment constraints.
For given $\bar x$, $m_{n-1}$, $m_n$
$$
\max_{f(x)} ...
2
votes
1answer
135 views
Need help with proof for arbitrage betting
Recently I came across this article about sports betting arbitrage: http://www.sportsbettingworm.com/arbitrage-calculations/index.html.
The article gives formulas for calculating arbitrage profit and ...
2
votes
1answer
48 views
Optimizing a physician's medical test plan
I have come across the following optimization problem:
"A patient presents himself with symptoms to a physician. The physician has a set of $n$ medical tests, where each test $i$ has costs $c_i$ ...
0
votes
1answer
14 views
online estimation of autoregressive process
I am interested about online estimation of autoregressive models. Is there anything I can find in the literature about this topic?
0
votes
1answer
74 views
what math topic is this kind of example part of? or what is needed to understand how to solve it? [closed]
we 100000000 sets/locations. each set has,
A = % chance of finding a cure (there are many different types of cures) for cancer
B = time it takes to extract a cure to caner
C = the optimal % chance (IN ...
0
votes
0answers
88 views
Differential Equations, Probability/Statistics, Optimization Problem - Relations?
While I am working on some physical/mathematical problems, I feel strongly that these three areas are almost the identical thing, except that they have different methods/from different aspects to ...
3
votes
1answer
116 views
Secretary problem for unknown n?
So one of my good friends is starting to date again (after being out of the country for two years), and I think that it might be helpful, or at least fun, to keep track of her dates in a ranked ...
0
votes
0answers
37 views
How to go about optimizing this function? (Maximizing)
If we are given a fixed integer $N > 0$ of choices we can pick out of a pool of $k$ values $c_0, \cdots, c_k$ (with repetitions allowed and $c_i > 0 \forall i$) and we want to maximize the ...
1
vote
2answers
37 views
Maximizing the time we reach to a threshold in a series of numbers
I have a problem and I really don't know what kind of mathematical method should I apply to solve or model my problem. I would be thankful If anyone can give me some answer or help.
Suppose we have ...
0
votes
1answer
38 views
Uniform Continuous R.V. - Optimization
working on this problem:
A road construction company needs to decide where to place an
emergency phone on a stretch of road of length L. Suppose that
accidents can happen uniformly at random ...
3
votes
0answers
78 views
Select positions for strongest defense given probability(position, target) scores. [closed]
In a game of tower defense, I want to place archers to optimize survival time.
I have ~10 towers, and I am allowed one archer per tower. The towers have 50 to 300 vantage points each. Once an archer ...
2
votes
2answers
512 views
One vs multiple servers - problem
Consider the following problem:
We have a simple queueing system with $\lambda%$ - probabilistic intensity of queries per some predefined time interval.
Now, we can arrange the system as a single ...
1
vote
1answer
104 views
Strategy to maximize no. of balls from N boxes
If you have N boxes each containing distinct number of balls and you are allowed to choose at most ...
3
votes
2answers
389 views
Grad degree that mainly deals with probability/game theory/optimization?
I'm currently working but am going to take classes as a non-degree student to beef up the math part of my background.
I've only taken calc 1-3, ODEs, linear algebra, logic, and decision theory so my ...
2
votes
2answers
79 views
is there a solution to the following maximization problem such that $a = b$?
Let $X = (X_1,...,X_n)$ be a vector of $n$ random variables.
Consider the following maximization problem:
$\max\limits_{a,b} \;\mathrm{Cov}(a\cdot X, b \cdot X)$ under the constraint that $\|a\|_2 = ...
1
vote
1answer
63 views
Derivatives with respect to a symmetric matrix, with an application to maximum likelihood
I am quite unsure about this whole matter of differentiation with respect to a matrix. First, I'd like a good (online hopefully) reference for getting up to speed on the theory - as opposed to a bunch ...
4
votes
4answers
103 views
Optimizing the expectancy
The following problem is about optimization. It is not a homework, but rather a natural question to ask to oneself afterwards. Here it is.
Consider a road of length $L$ between two cities $A$ and ...
7
votes
1answer
179 views
Stochastic assignment problem
Given an $n \times n$ real matrix $C$, we can try to maximize
$$\Phi(C, \pi) = \frac{1}{n} \sum_{i} C_{i,\pi(i)}
$$
over $\pi \in S_n$, the set of all permutations on $n$ objects. What can one say ...
7
votes
1answer
295 views
Manifold with minimum surface distance between two points
The book "The World is Flat" uses flatness as a metaphor for a global economy. In fact, a spherical world would seem to be better than a flat world in terms of reducing the distances between two ...
7
votes
2answers
323 views
Generalization of the Sultan's dowry problem
We know the solution of the Sultan's dowry problem:
To reject the first $n/e$ candidates and then to select the first who exceeds the best of the sample.
How to find the best strategy if we want ...
2
votes
1answer
164 views
Maximize normal density function over a subset
For a 2D Normal distribution $N(0, \left[ \begin{array}{cc} 1 & -1/4 \\ -1/4 & 1 \end{array} \right])$, I am now trying to maximize its density function over $\{ x\geq 10, y \geq 10 \}$.
My ...
3
votes
3answers
411 views
Optimally combining samples to estimate averages
Suppose I have two tables, each of unknown size, and I'd like to estimate the average of their true sizes. I hire 2 contractors: one guarantees good precision (i.e., her measurement ...
