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This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded…
We study power utility maximization for exponential L\'evy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the L\'evy triplet is…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
We axiomatically define a cardinal social inefficiency function, which, given a set of alternatives and individuals' vNM preferences over the alternatives, assigns a unique number -- the social inefficiency -- to each alternative. These…
The usual theory of inflation breaks down in eternal inflation. We derive a dual description of eternal inflation in terms of a deformed Euclidean CFT located at the threshold of eternal inflation. The partition function gives the amplitude…
It has become standard practice to take the logarithmic growth of the scale factor as a measure of the amount of inflation, despite the well-known fact that this is only an approximation for the true amount of inflation required to solve…
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 consider the problem of optimal consumption from labor income and investment in a general incomplete semimartingale market. The economic agent cannot borrow against future income, so the total wealth is required to be positive at (all or…
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 study a minimalist kinetic model for economies. A system of agents with local trading rules display emergent demand behaviour. We examine the resulting wealth distribution to look for non-thermal behaviour. We compare and contrast this…
We analyze a conservative market model for the competition among economic agents in a close society. A minimum dynamics ensures that the poorest agent has a chance to improve its economic welfare. After a transient, the system…
We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization…
In [1] we presented a model for transactions when goods are given away in the expectation of a later settlement. In settings where people keep track of their social accounts we were able to redefine concepts like account balance, yield…
We propose the introduction of a Heisenberg symmetry of the Kahler potential to solve the problems with chaotic inflation in supergravity, as a viable alternative to the use of shift symmetry. The slope of the inflaton potential emerges…
We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time…
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are…
The productivity of a common pool of resources may degrade when overly exploited by a number of selfish investors, a situation known as the tragedy of the commons (TOC). Without regulations, agents optimize the size of their individual…
Motivated by the impact of emerging technologies on toll parks, this paper studies a problem of equilibrium, social welfare, and revenue for an infinite-server queue. More specifically, we assume that a customer's utility consists of a…
Inflationary models, especially those with plateau-type potentials, are consistent with the cosmological data, but inflation itself does not resolve the initial singularity. This singularity is resolved, for example, by the idea of the…
We consider an optimal control problem arising in the context of economic theory of growth, on the lines of the works by Skiba (1978) and Askenazy - Le Van (1999). The economic framework of the model is intertemporal infinite horizon…