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We construct analytic and numerical solutions of the Fokker-Planck equation that arises in the context of stochastic inflation. We use these solutions to derive necessary conditions for eternal inflation on the higher derivatives of the…
Two qualitatively different modes of ending superluminal expansion are possible in extended inflation. One mode, different from the one envoked in most extended models to date, easily avoids making big bubbles that distort the cosmic…
The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate…
We offer mathematical tractability and new insights for a framework of exponential utility with non-negative consumption, a constraint often omitted in the literature giving rise to economically unviable solutions. Specifically, using the…
Many countries impose regulatory restrictions on lending rates known as interest rate caps. In most cases, these restrictions apply to the effective (rather than nominal) interest rate, a measure which incorporates all commissions and fees…
The meaning of the inflationary slow-roll approximation is formalised. Comparisons are made between an approach based on the Hamilton-Jacobi equations, governing the evolution of the Hubble parameter, and the usual scenario based on the…
Traditionally, inflationary models are analyzed in terms of parameters such as the scalar spectral index ns and the tensor to scalar ratio r, while dark energy models are studied in terms of the equation of state parameter w. Motivated by…
During the inflationary epoch,geometry of the universe may be described by quasi-de Sitter space. On the other hand,maximally extended de Sitter metric in the comoving coordinates accords with a special FLRW model with positive spatial…
We provide four novel results for nonhomothetic Constant Elasticity of Substitution preferences (Hanoch, 1975). First, we derive a closed-form representation of the expenditure function of nonhomothetic CES under relatively flexible…
Monetary inflation is a sustained increase in the money supply than can result in price inflation, which is a rise in the general level of prices of goods and services. The objectives of this paper were to develop economic models to (1)…
The potential during inflation must be very flat in, at least, the direction of the inflaton. In renormalizable global supersymmetry, flat directions are ubiquitous, but they are not preserved in a generic supergravity theory. It is known…
We develop a new class of chaotic inflation models with spontaneously broken conformal invariance. Observational consequences of a broad class of such models are stable with respect to strong deformations of the scalar potential. This…
We show how a stochastic version of the Lagrange multiplier method can be combined with the stochastic maximum principle for jump diffusions to solve certain constrained stochastic optimal control problems. Two different terminal…
We explore possible constraints on the inflationary equation state: p=w\rho. While w must be close to -1 for those modes that contribute to the observed power spectrum, for those modes currently out of experimental reach, the constraints on…
We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex…
The Lambert W function has utility for solving various exponential and logarithmic equations arranged in the form of $g(x)e^{g(x)}$. Using the Lambert W function and tetration, a variety of categorized inversion formulas are presented.…
We note that the essential idea of inflation, that the universe underwent a brief period of accelerated expansion followed by a long period of decelerated expansion, can be encapsulated in a "closure condition" which relates the amount of…
A natural combination of the first and second derivatives of the scalar potential was achieved in a framework of an alternative refined de Sitter conjecture recently proposed in the literature. In this work, we study various inflation…
Toy models for the Hubble rate or the scalar field potential have been used to analyze the amplification of scalar perturbations through a smooth transition from inflation to the radiation era. We use a Hubble rate that arises consistently…
A thin wall approximation is exploited to describe a global monopole coupled to gravity. The core is modelled by de Sitter space; its boundary by a thin wall with a constant energy density; its exterior by the asymptotic Schwarzschild…