Abstract This paper focuses on modeling the dynamics of a stockless market using piecewise smooth dynamical systems combined with stochastic processes. The proposed models describe market behavior through ordinary differential equations that incorporate key variables such as offer, demand, and developing production capacity; these equations exhibit discontinuities in specific regions, representing abrupt changes in investment decisions based on expected returns. The introduction of randomness via piecewise deterministic Markov processes allows us to model uncertainties and stochastic behavior in the investment decision-making process. The model establishes the existence of fold-fold singularities, points where two tangencies intersect, highlighting critical transitions in market dynamics, including sudden changes in prices and shifts in offer and demand behavior. Numerical simulations support the theoretical results, illustrating the trajectories near switching surfaces and within sliding regions; this study contributes to a deeper understanding of how discontinuities and singularities in mathematical models can impact market stability and emphasizes the role of piecewise smooth systems and stochastic processes in economic modeling and decision-making.
Olivar et al. (Mon,) studied this question.