arXiv subjects

Mario Cavani

Publications and source records attributed to Mario Cavani.

3 recordsLinked to original sources

arXiv2026

The fused asset flow model: stability, bifurcation, and contagion in multi-asset markets with heterogeneous investors

This paper presents a unified multi-asset, multi-group asset-flow model that integrates three foundational frameworks from the behavioral finance literature. The model captures the dynamics of financial markets where multiple assets are traded by multiple investor groups, each with distinct trend-following (momentum) and value-based (fundamental) strategies. Unlike classical efficient market models, our framework explicitly incorporates the finiteness of cash and shares, asymmetric cross-asset coupling in buying decisions, and endogenous wealth redistribution across groups. We derive the complete system of ordinary differential equations governing price, cash, share, and sentiment dynamics, and establish the fundamental properties of positivity and boundedness for all physically relevant variables. The equilibrium set is characterized as a manifold parameterized by cash distribution, with the fundamental equilibrium as a special point. Through linear stability analysis, we identify conditions under which the fundamental equilibrium loses stability via a supercritical Hopf bifurcation, giving rise to persistent limit cycles. The model is validated against three benchmark papers: the single-asset multi-group model of DeSantis, Swigon, and Caginalp (2012); the two-asset single-group model of Bulut, Merdan, and Swigon (2019); and the two-asset two-group Nigeria-Libya oil market model of Cavani (2026). Our numerical simulations reproduce all key theoretical predictions, including equilibrium manifolds, Hopf bifurcation thresholds, limit cycle periods, and asymmetric contagion patterns.

math.DS↗

arXiv2026

A Microeconomic Finance Model with a Multi-Asset Market and a Multi-Investor Heterogeneous Groups

We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed amount of cash and shares (no additions are allowed over time, so the system is closed), and the trading groups are influenced by trend and valuation motivations when buying or selling each asset, but follow a strategy where the purchase of one asset depends on the price of another, while the sale does not. Using these assumptions and basic microeconomic principles, the mathematical model is derived using a dynamic systems approach. We analyze the stability of the model's equilibrium points and determine the parameter conditions for such stability. First, we show that all equilibria are stable in the absence of a clear emphasis on trend-based valuation for each share. Secondly, for systems where the trading group prioritizes the valuation of each stock and the trend of the other for trading purposes, we establish stability conditions and demonstrate with numerical examples that when instability occurs, it manifests as price oscillations in the stocks. Furthermore, we argue for the existence of periodic solutions via a Hopf bifurcation, taking the momentum coefficient as the bifurcation parameter. Finally, we present examples and numerical simulations to support and expand upon the analytical results. One finding in economics and finance is the existence of cyclical behavior in the absence of exogenous factors, as determined by the momentum coefficient. In particular, a stable equilibrium price becomes unstable as trend-based trading increases.

math.DS↗

arXiv2025

A Method to Estimate a Neighborhood of a Periodic Orbit

In this paper we describe a method to estimate a neighborhood containing a periodic orbit of a given system of two ordinary differential equations. By using the theory of integral averages, the system of differential equations can be transformed into an equivalent autonomous system which, by using the Hopf bifurcation theorem, the existence of a periodic solution of this autonomous nonlinear differential equations can be demonstrated. Using of this procedure it is possible to estimate an annular region where the orbit of the periodic solution is located. The method allows to improve the results that the Hopf Bifurcation provides on periodic solutions. In addition, some quantitative characteristics of the solution can be known, such as the amplitude, the period and, a region where the periodic orbit of the original system is located. The method is applied to a three-dimensional system of differential equations that models the competition of two predators and one prey, which under the assumption that the predators are equally voracious, property that in this case leads to a two-dimensional system, where all of the conditions of the method described here are easily applicable.

math.DS↗