Ambiguity, No Arbitrage, Coherence and Artificial Financial Markets

In many traditional financial and economic models, economic agents are assumed to make decisions using expected lifetime utility under rational expectations, where rational expectations are assumed to be formed on the basis of sufficient knowledge of the data generating process. But the mere existence of econometricians modelling and estimating data generating (risky) processes already indicates the presence of ambiguity on the `true' data generating (possibly non-risky) process. There might be ambiguity because of sampling error (due to estimation), but there might also be ambiguity resulting from potential modelling error (due to a wrong choice of model class describing the data generating process). Rational agents will (try to) incorporate such ambiguity when making their decisions. In this paper we first investigate the implications for modelling asset prices in financial markets under the assumption of no arbitrage when there is ambiguity. We argue that coherence, as introduced by Shafer and Vovk (2001), becomes the guiding principle in modelling financial markets without arbitrage opportunities. Next, we illustrate that artificial financial markets, that can be investigated using microscopic simulation techniques, is a natural way to study coherent financial markets under ambiguity