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As described in the comments, you could maybe count instances in probability theory, econometrics, PDEs, or numerical analysis. But in general, besides using trivial properties of complex numbers (as …

Edesess is attacking what is really just a straw man of economics. I'm not sure he really understands the field. To start, economics is not math. We're not claiming that it is. It's more of an "applie …

P being negative semi-definite would imply that V is a concave function. The reason you would restrict P so that V would be a concave function is because of some of the assumptions you've made about a …

Here's my best guess. I haven't checked to thoroughly if this is right, but maybe it will help. Evolution of population density I understand the model as follows. $f(a,t)$ is the density of people o …

$\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\dd}{\, \mathrm{d}}$ How many arguments does $C$ have? If the only argument to $C$ is $Y_D$, then $C_Y$ and $C_\tau$ might not make se …

The question is broad, but I believe there is plenty of literature that defines this concept in similarly broad terms. The following is adapted from the Wikipedia on Pareto Efficiency, which is the ma …

I have more often heard of how the Black-Scholes equation is just the heat equation. You can find that information here. I haven't heard of a relationship between Black-Scholes and quantum mechanics b …

Once you have solved the equation $\rho V(k) = \max_c g(c) + V'(k)(z - c)$ to find the function $V(k)$ you should be able to solve for what is called the policy function. The function $V(k)$ is the va …

They are related and usually fall into the same discussion, but as @Alecos mentions in the comments, the two theorems show different things. I suppose the connection that you're after is the fact tha …

I once heard Roger Myerson talk about why he thought Economics has, as a Social Science, been so successful in applying (or has so readily incorporated) mathematics. He suggested that perhaps it was d …

A lot of mathematicians and, here, computer scientists study open problems in game theory. Here is an article that talks about the potential solution of an open problem in mechanism design: http://new …

I've been meaning to post this for a long time. I came across this and thought it could add some insight. This example is from "Financial Asset Pricing Theory" by Munk. Consider the following figure. …

The fact that you ask about "safety" implies that you believe that some result is in jeopardy. This answer can be improved if you can specify a result that you might have in mind. Otherwise, take as a …