Related papers: The puzzle that just isn't
In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture…
A number of phenomena generally believed characteristic of quantum mechanics and seen as interpretively problematic--the incompatibility and value-indeterminacy of variables, the non-existence of dispersion-free states, the failure of the…
We review locked inflation and we critically address phenomenological and consistency issues thathave appeared in the literature. A natural window of opportunity is found for the original scenario.Moreover, a simple way to enlarge the…
We study inflation within the framework of non-canonical scalar field. In this scenario, we obtain the inflationary observables such as the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index as well…
This paper considers the nonlinear theory of G-martingales as introduced by Peng. A martingale representation theorem for this theory is proved by using the techniques and the results established in an accompanying paper for the second…
In the present work we prove a number of surprising results about gaps between consecutive primes and arithmetic progressions in the sequence of generalized twin primes which could not have been proven without the recent fantastic…
Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure…
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…
Identifying behavior that is relatively invariant under different conditions is a challenging task in far-from-equilibrium complex systems. As an example of how the existence of a semi-invariant signature can be masked by the heterogeneity…
Valuation and parity formulas for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, possibility of default and "bubbles" in asset prices. The formulas are given via…
A very brief history of relative valuation in neoclassical finance since 1973 is presented, with attention to core currency issues for emerging economies. Price formation is considered in the context of hierarchical causality, with…
A wide variety of vacua, and their cosmological realization, may provide an explanation for the apparently anthropic choices of some parameters of particle physics and cosmology. If the probability on various parameters is weighted by…
Behavior of systems that are functions of anticipated behavior of other systems, whose own behavior is also anticipatory but homeostatic and determined by hierarchical ordering, which changes over time, of sets of possible environments that…
We study a game where households convert paper assets, such as money, into consumption goods, to preempt inflation. The game features a unique equilibrium with high (low) inflation, if money supply is high (low). For intermediate levels of…
We discuss a non-intuitive situation concerning percentages.
The nature of monetary arrangements is often discussed without any reference to its detailed construction. We present a graph representation that allows for a clear understanding of modern monetary systems. First, we show that systems based…
In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders getting to be influenced by the other traders' investment attitudes…
We consider the spectrum of primordial fluctuations produced by inflationary models where the inflaton potential is the sum of two exponential terms. A wide range of spectra result, with the only constraint being that the scalar spectrum…
In the inflationary era, black holes came into existence together with the universe through the quantum process of pair creation. We calculate the pair creation rate from the no boundary proposal for the wave function of the universe. Our…
The St. Petersburg Paradox, an important topic in probability theory, has not been solved in the last 280 years. Since Nicolaus Bernoulli proposed the St. Petersburg Paradox in 1738, many people had tried to solve it and had proposed…