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The potential of machine learning to automate and control nonlinear, complex systems is well established. These same techniques have always presented potential for use in the investment arena, specifically for the managing of equity…
The capitalization-weighted total relative variation $\sum_{i=1}^d \int_0^\cdot \mu_i (t) \mathrm{d} \langle \log \mu_i \rangle (t)$ in an equity market consisting of a fixed number $d$ of assets with capitalization weights $\mu_i (\cdot)$…
We review the statistical mechanics approach to the study of the emerging collective behavior of systems of heterogeneous interacting agents. The general framework is presented through examples is such contexts as ecosystem dynamics and…
A financial system contains many elements networked by their relationships. Extensive works show that topological structure of the network stores rich information on evolutionary behaviors of the system such as early warning signals of…
The evaluation of the financial markets to predict their behaviour have been attempted using a number of approaches, to make smart and profitable investment decisions. Owing to the highly non-linear trends and inter-dependencies, it is…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
This paper studies a discrete-time version of the Lucas-Uzawa endogenous growth model with physical and human capital in the presence of externalities. Existence of an optimal equilibrium is proved using tools from dynamic programming with…
Pseudo panels constituted with repeated cross-sections are good substitutes to true panel data. But individuals grouped in a cohort are not the same for successive periods, and it results in a measurement error and inconsistent estimators.…
We present a dynamical theory of asset price bubbles that exhibits the appearance of bubbles and their subsequent crashes. We show that when speculative trends dominate over fundamental beliefs, bubbles form, leading to the growth of asset…
We select n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We analyze each ensemble of stock returns by…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
The article is focused on studying how to predict the failure times of coherent systems from the early failure times of their components. Both the cases of independent and dependent components are considered by assuming that they are…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…
Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization…
Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly…
Proving the existence of speculative financial bubbles even a posteriori has proven exceedingly difficult so anticipating a speculative bubble ex ante would at first seem an impossible task. Still as illustrated by the recent turmoil in…
We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…
Time series forecasting plays an increasingly important role in modern business decisions. In today's data-rich environment, people often aim to choose the optimal forecasting model for their data. However, identifying the optimal model…
Previous work on fantasy basketball has established methods for optimizing team construction for head-to-head formats. This has been facilitated by the straightforwardness of calculating the objective function for those formats, given that…