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In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic market models: the Levy\u2013Levy\u2013Solomon model and the Franke\u2013Westerhoff model. We derive time-continuous formulations of both models, and in particular, we discuss the impact of the time-scaling on the model behavior for the Levy\u2013Levy\u2013Solomon model. For the Franke\u2013Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model. Furthermore, we discuss possible probabilistic descriptions of time-continuous agent-based computational economic market models. Especially, we present the potential advantages of kinetic theory in order to derive mesoscopic descriptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy\u2013Levy\u2013Solomon and Franke\u2013Westerhoff model.<\/jats:p>","DOI":"10.1142\/s0219525920500174","type":"journal-article","created":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T15:41:07Z","timestamp":1619538067000},"page":"2050017","source":"Crossref","is-referenced-by-count":0,"title":["ROBUST MATHEMATICAL FORMULATION AND PROBABILISTIC DESCRIPTION OF AGENT-BASED COMPUTATIONAL ECONOMIC MARKET MODELS"],"prefix":"10.1142","volume":"23","author":[{"given":"MAXIMILIAN","family":"BEIKIRCH","sequence":"first","affiliation":[{"name":"RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SIMON","family":"CRAMER","sequence":"additional","affiliation":[{"name":"WZL, RWTH Aachen University, Campus-Boulevard 30, 52074 Aachen, 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