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Continuous optimization

I'm interested in the solution to the following problem: I have initial capital $C$ which I can invest into $M$ classes of resources, each unit of a class $m_i$ matures at time $t_i$, has a return of ...
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To what equal constant in the Gibbs lemma

The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is: Lemma (Gibbs). $f_1,f_2,\ldots,f_n$ be ...
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A categorical analogue of Debreu's independent factors theorem

Background A major question in Decision Theory is that of the cardinal meaning of a utility function. That is, given a set $X$, a utility function $u:X\rightarrow \mathbb{R}$ represents the choices ...
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Maximizing Expected Utility

I am currently trying to solve a maximization problem given by $\max_{f(x)} \int_0^1 \int_\mathbb{R} (c-y\cdot f(x)-d\cdot (x+f(x)-b)^2) \ h(x) \ dx \ dy$. Or in other words, I have a utility ...
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Why does the OLS estimator simplify as follows for the single regressor case?

I was reading in "A Guide to Econometrics" that given $Y = X \beta + \epsilon$, the variance covariance matrix of $\beta^\text{OLS}$ is given by $\sigma^2 (X' X)^{-1}$ where $\sigma^2$ is the variance ...