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The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…
We examine the stationary distribution of random walks on directed graphs. In particular, we focus on the {\em principal ratio}, which is the ratio of maximum to minimum values of vertices in the stationary distribution. We give an upper…
For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows to construct new distributions with support (0,1), and to obtain a…
We develop a mean-field theory of the growth, exchange and distribution (GED) model introduced by Kang et al. (preceding paper) that accurately describes the phase transition in the limit that the number of agents $N$ approaches infinity.…
Mounting evidences are being gathered suggesting that income and wealth distribution in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, but also deviating…
We develop a dual-control method for approximating investment strategies in incomplete environments that emerge from the presence of trading constraints. Convex duality enables the approximate technology to generate lower and upper bounds…
We consider a model of directed polymers on regular trees with complex-valued random weights introduced by Cook and Derrida [CD90] and studied mathematically by Derrida, Evans and Speer [DES93]. In addition to the usual weak-disorder and…
This paper proposes a distributed algorithm to find the Nash equilibrium in a class of non-cooperative convex games with partial-decision information. Our method employs a distributed projected gradient play approach alongside consensus…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic…
The problem of allocating scarce items to individuals is an important practical question in market design. An increasingly popular set of mechanisms for this task uses the concept of market equilibrium: individuals report their preferences,…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
We derive the joint density of market weights, at fixed times and suitable stopping times, of the volatility-stabilized market models introduced by Fernholz and Karatzas in [Ann. Finan. 1 (2005) 149-177]. The argument rests on computing the…
I show that U.S. incomes follow a one-parameter family of probability distributions over more than fifty years of data. I compare statistical models of income, and I highlight the inverse-gamma distribution as a parsimonious model that…
This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed…
We present a simplified model for the exploitation of finite resources by interacting agents, where each agent receives a random fraction of the available resources. An extremal dynamics ensures that the poorest agent has a chance to change…
As a model of market price, we introduce a new type of random walk in a moving potential which is approximated by a quadratic function with its center given by the moving average of its own trace. The properties of resulting random walks…
The paper provides a survey of results related to the "$\kappa$-generalized distribution", a statistical model for the size distribution of income and wealth. Topics include, among others, discussion of basic analytical properties,…
The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the…