Related papers: Market shape formation, statistical equilibrium an…
Decisions taken in our everyday lives are based on a wide variety of information so it is generally very difficult to assess what are the strategies that guide us. Stock market therefore provides a rich environment to study how people take…
We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The…
Stochastic portfolio theory aims at finding relative arbitrages, i.e. trading strategies which outperform the market with probability one. Functionally generated portfolios, which are deterministic functions of the market weights, are an…
This paper suggests that business cycles may be a manifestation of coupled real economy and stock market dynamics and describes a mechanism that can generate economic fluctuations consistent with observed business cycles. To this end, we…
As a typical representation of complex networks studied relatively thoroughly, financial market presents some special details, such as its nonconservation and opinions spreading. In this model, agents congregate to form some clusters, which…
This note studies a certain stochastic evolution equation in the space of probability measures, including existence and uniqueness results. A solution of this equation gives rise, in a natural way, to an interest rate term structure model,…
This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…
In this chapter, an input-output economic model with multiple interactive economic systems is considered. The model captures the multi-dimensional nature of the economic sectors or industries in each economic system, the interdependencies…
Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these…
The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is…
We provide closed-form market equilibrium formula consolidating informational imperfections and investors beliefs. Based on Merton's model, we characterize the equilibrium expected excess returns vector with incomplete information. We then…
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…
We propose a class of Markovian agent based models for the time evolution of a share price in an interactive market. The models rely on a microscopic description of a market of buyers and sellers who change their opinion about the stock…
In this paper we continue the study of the simulated stock market framework defined by the driving sentiment processes. We focus on the market environment driven by the buy/sell trading sentiment process of the Markov chain type. We apply…
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
Asset exchange models (AEMs) provide a physics-inspired framework for studying wealth formation. These models capture wealth distribution dynamics via pairwise money exchanges, yielding steady-state distributions from exponential to…