Related papers: A note on the Cobb-Douglas function
Let $n\ge1$ and $B\ge2$. A real-valued function $f$ defined on the $n$-simplex $\Delta_n$ is approximately convex with respect to $\Delta_{B-1}$ iff f(\sum_{i=1}^B t_ix_i) \le \sum_{i=1}^B t_if(x_i) +1 for all $x_1,...,x_B \in \Delta_n$ and…
We give a sufficient and necessary condition for a probability measure $\mu$ on the real line to satisfy the logarithmic Sobolev inequality for convex functions. The condition is expressed in terms of the unique left-continuous and…
Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic…
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…
The standard framing treats structured human-data work as transitional, a bridge between today's imperfect models and a future state where automation is complete. We challenge this view by modeling structured human data as a persistent…
The valuation process that economic agents undergo for investments with uncertain payoff typically depends on their statistical views on possible future outcomes, their attitudes toward risk, and, of course, the payoff structure itself.…
We develop an information-theoretic framework for discrete dynamics grounded in a comparison-cost functional on ratios. Given two quantities compared via their ratio \(x=a/b\), we assign a cost \(F(x)\) measuring deviation from equilibrium…
The idea of ``dynamically'' generated parton distribution functions, based on regular initial conditions at low momentum scale, is reanalyzed with particular emphasize paid to its compatibility with the factorization mechanism. Basic…
I show that if the capital accumulation dynamics is stochastic a new term, in addition to that given by accounting prices, has to be introduced in order to derive a correct estimate of the genuine wealth of an economy. In a simple model…
In this paper we give an alternative proof for a vanishing result about flat functions proved in G.Stoica, "When must a flat function be identically zero", The American Mathematical Monthly 125(7)648-649,2018. With a dynamical approach we…
Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the…
Constant and symmetric price impact functions, most commonly used in agent-based market modelling, are shown to give rise to paradoxical and inconsistent outcomes in the simplest case of arbitrage exploitation when open-hold-close actions…
We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order…
The possibility of the global Lagrangian reduction of a mechanical system with symmetry is shown to be connected with the characteristic class of a principal fiber bundle of the configuration space over the factor manifold. It is proved…
The minimization of a multiobjective Lagrangian with non-constant discount is studied. The problem is embedded into a set-valued framework and a corresponding definition of the value function is given. Bellman's optimality principle and…
We study Lebesgue integration of sums of products of globally subanalytic functions and their logarithms, called constructible functions. Our first theorem states that the class of constructible functions is stable under integration. The…
Connections are made between solution concepts for games in characteristic function form and Euler's Theorem underlying the neo-classical theory of distribution in which the total output produced is imputed to the marginal products of the…
We analyze the stability of general nonlinear discrete-time stochastic systems controlled by optimal inputs that minimize an infinite-horizon discounted cost. Under a novel stochastic formulation of cost-controllability and detectability…
This paper presents a new nested production function that is specifically designed for analyzing capital and labor intensity of manufacturing industries in developing and developed regions. The paper provides a rigorous theoretical…
A recursive function on a tree is a function in which each leaf has a given value, and each internal node has a value equal to a function of the number of children, the values of the children, and possibly an explicitly specified random…