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Abstract<br/>Firstly, the asynchronous discrete cadlag feature of price and order time series demands causal structuring.<br/>We determine the waiting time between two successive market events by an approach that might<br/>be named doubly stochastic Markov process, analogously to doubly stochastic Poisson process. The assumption<br/>of a time-continuous and -homogeneous conservative Markov process leads to waiting times<br/>following an exponential distribution. Its state dependent parameter is governed by the dynamics of<br/>the Markov process. Secondly, in our model the state transition is not constant, but controlled by the<br/>probability that the acting agent takes the action which generates the transition. Thirdly, the probability<br/>for placing buy or sell orders is determined according to the willingness to pay concept of discrete<br/>choice models based on random utility. The causal foundation of the model relies on the basic principle:<br/>The higher the utility of an activity, the higher the probability of taking this activity, and the shorter the<br/>expected waiting time. Simulated price and order time series are presented.<br/>Keywords: Doubly Stochastic Markov Process; Random Utility Maximization; Interacting agents; Market<br/>Microstructure; Order book simulation; Quantitative-Behavioural Finance<br/><br/>
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