Related papers: Elephant random walk with attributed steps and ext…
In Robbins' problem of minimizing the expected rank, a finite sequence of $n$ independent, identically distributed random variables are observed sequentially and the objective is to stop at such a time that the expected rank of the selected…
This paper considers two investors who perform mean-variance portfolio selection with asymmetric information: one knows the true stock dynamics, while the other has to infer the true dynamics from observed stock evolution. Their portfolio…
We consider two competing first passage percolation processes started from uniformly chosen subsets of a random regular graph on $N$ vertices. The processes are allowed to spread with different rates, start from vertex subsets of different…
Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…
There are two possible ways of interpreting the seemingly stochastic nature of financial markets: the Efficient Market Hypothesis (EMH) and a set of stylized facts that drive the behavior of the markets. We show evidence for some of the…
Let $(S_n^p)_{n\geq 0}$ be a Bernoulli random walk where each of the independent increments is either $1$ or $-1$ with probabilities $p$ and $1-p$. For $p'$ and $p'' \in [0,1]$ with $|p'-1/2|>|p''-1/2|$, we show that $(|S_n^{p''}|)_{n\geq…
The Random Utility Maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behavior, such as halo effects, that…
In stochastic combinatorial optimization, algorithms differ in their adaptivity: whether or not they query realized randomness and adapt to it. Dean et al. (FOCS '04) formalize the adaptivity gap, which compares the performance of fully…
Gut and Stadm\"{u}ller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an extension of results by Gut and Stadtm\"{u}ller (2022) for an…
Deterministic walk in an excited random environment is a non-Markov integer-valued process $(X_n)_{n=0}^{\infty}$, whose jump at time $n$ depends on the number of visits to the site $X_n$. The environment can be understood as stacks of…
We study generalizations of online bipartite matching in which each arriving vertex (customer) views a ranked list of offline vertices (products) and matches to (purchases) the first one they deem acceptable. The number of products that the…
Firms compete for clients, creating distributions of market shares ranging from domination by a few giant companies to markets in which there are many small firms. These market structures evolve in time, and may remain stable for many years…
Traditional approaches to ranking in web search follow the paradigm of rank-by-score: a learned function gives each query-URL combination an absolute score and URLs are ranked according to this score. This paradigm ensures that if the score…
We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…
In this communication, some economic models given by functional mappings are addressed. These are models for random markets where agents trade by pairs and exchange their money in a random and conservative way. They display the exponential…
We present a graph-theoretic model of consumer choice, where final decisions are shown to be influenced by information and knowledge, in the form of individual awareness, discriminating ability, and perception of market structure. Building…
We study the long time behavior of the elephant random walk with stops, introduced by Kumar, Harbola and Lindenberg (2010), and establish the phase transition of the number of visited points up to time $n$, and the correlation between the…
The Elephant Random Walk (ERW), first introduced by Sch\"utz and Trimper (2004), is a one-dimensional simple random walk on $ \mathbb{Z} $ having a memory about the whole past. We study the Shark Random Swim, a random walk whose steps are $…
We continue our study of the unidirectional elephant random walk (uERW) initiated in {\it {Electron. Commun. Probab.}} ({\bf 29} 2024, article no. 78). In this paper we obtain definitive results when the memory exponent $\beta\in (-1,…
We study the win rate $R_{N_d}/N_d$ of a biased simple random walk $S_n$ on $\mathbb{Z}$ at the first-passage time $N_d=\inf\{n\ge 0:S_n=d\}$, with $p=P[X_1=+1]\in[1/2,1)$. Using generating-function techniques and integral representations,…