This article considers three standard asset pricing models with adaptive agents and stochastic dividends. The models only differ in the parameters to be estimated. We assume that only limited information is used to construct estimators. Therefore, parameters are not estimated consistently. More precisely, we assume that the parameters are estimated by exponential smoothing, where past parameters are down-weighted and the weight of recent observations does not decrease with time. This situation is familiar for applications in finance. Even if time series of volatile stocks or bonds are available for a long time, only recent data is used in the analysis. In this situation the prices do not converge and remain a random variable. This raises the question how to describe equilibrium behavior with stochastic prices. However, prices can reveal properties such as ergodicity, such that the law of the price process converges to a stationary law, which provides a natural and useful extension of the idea of equilibrium behavior of an economic system for a stochastic setup. It is this implied law of the price process that we investigate in this paper. We provide conditions for the ergodicity and analyze the stationary distribution. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

In this article we investigate the question whether the highly demanding informative requirements of rational expectations models are necessary to derive equilibria within capital market models. In the analysis agents are only provided with publicly available information such as prices and dividends. Nevertheless, we require that agents should behave like econometricians. Additionally, we skip the assumption of rational expectations models that agents know the implied law of motion of the system. By these assumptions, the stock market can be considered as a Sorger-Hommes consistent expectations model. In this article, we show the existence of consistent expectations equilibria with myopic agents, where the only CEE is the rational expectations equilibrium. In the simulation part we demonstrate how the steady state CEE can be derived by means of sample autocorrelation learning. Thus, we are able to derive a stock market equilibrium with less demanding requirements, where this equilibrium is equal to the rational expectations equilibrium. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Adaptive agent models are supposed to result in the same limit behavior as models with perfectly rational agents. In this article we show that this claim cannot by accepted in general, even in a simple capital market model, where the agents apply sample autocorrelation learning to perform their forecasts. By applying this learning algorithm, the agents use sample means, the sample autocorrelation coefficient, and the sample variances of prices to predict the future prices, and to determine the demand for the risky asset. Therefore, even if the agents are not perfectly rational, we require that the agents' forecasts are consistent with the underlying information. In this article a sufficient condition for convergence is derived analytically, and checked by means of simulations. The price sequence as well as the sequence of parameters - estimated by means of sample autocorrelation learning - converge, if the initial value of the price sequence is sufficiently close to the steady-state equilibrium, and a random variable derived from the dividend process is not too volatile to skip the price trajectory out of the attracting region. Therefore, the market price can even diverge, and the region of convergence could become very small depending on the underlying parameters. Thus, divergence of the price sequences is not a pathological example, since it possibly occurs over a wide range of parameters. Therefore, the often claimed coincidence of adaptive agents models and ration agent models cannot be observed even in a simple capital market model. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Various studies of asset markets have shown that traders are capable of learning and transmitting information through prices in many situations. In this paper we replace human traders with intelligent software agents in a series of simulated markets. Using these simple learning agents, we are able to replicate several features of the experiments with human subjects, regarding (1) dissemination of information from informed to uninformed traders, and (2) aggregation of information spread over different traders.

This paper studies the dynamics of an asset pricing model based on simple deterministic agents. Traders are heterogeneous with respect to their time horizon, prediction function and trade interval. Concerning the trade interval we distinguish between intraday traders and end-of-day traders. Intraday traders update their portfolio every period, whereas end-of-day traders adjust their positions only at the closing price of each trading day. The parameter values of the model were partially determined by an adapted Markov chain Monte Carlo sampling method. We analyse the properties of the time series and find that they exhibit low autocorrelation of the returns, volatility clustering and fat tails. Particularly heterogeneous trade intervals seem to be an important factor for generating time series showing "stylized facts". (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Market microstructure studies the process of exchanging assets underexplicit trading rules. With algorithmic trading and high-frequencytrading, modern financial markets have seen profound changes in marketmicrostructure in the last 5 to 10 years. As a result, previously establishedmethods in the field of market microstructure becomes oftenfaulty or insufficient. Machine learning and, in particular, reinforcementlearning has become more ubiquitous in both finance and otherfields today with applications in trading and optimal execution. This thesisuses reinforcement learning to understand market microstructureby simulating a stock market based on NASDAQ Nordics and trainingmarket maker agents on this stock market. Simulations are run on both a dealer market and a limit orderbook marketdifferentiating it from previous studies. Using DQN and PPO algorithmson these simulated environments, where stochastic optimal controltheory has been mainly used before. The market maker agents successfullyreproduce stylized facts in historical trade data from each simulation,such as mean reverting prices and absence of linear autocorrelationsin price changes as well as beating random policies employed on thesemarkets with a positive profit & loss of maximum 200%. Other tradingdynamics in real-world markets have also been exhibited via theagents interactions, mainly: bid-ask spread clustering, optimal inventorymanagement, declining spreads and independence of inventory and spreads, indicating that using reinforcement learning with PPO and DQN arerelevant choices when modelling market microstructure. / Marknadens mikrostruktur studerar hur utbytet av finansiella tillgångar sker enligt explicita regler. Algoritmisk och högfrekvenshandel har förändrat moderna finansmarknaders strukturer under de senaste 5 till 10 åren. Detta har även påverkat pålitligheten hos tidigare använda metoder från exempelvis ekonometri för att studera marknadens mikrostruktur. Maskininlärning och Reinforcement Learning har blivit mer populära, med många olika användningsområden både inom finans och andra fält. Inom finansfältet har dessa typer av metoder använts främst inom handel och optimal exekvering av ordrar. I denna uppsats kombineras både Reinforcement Learning och marknadens mikrostruktur, för att simulera en aktiemarknad baserad på NASDAQ i Norden. Där tränas market maker - agenter via Reinforcement Learning med målet att förstå marknadens mikrostruktur som uppstår via agenternas interaktioner. I denna uppsats utvärderas och testas agenterna på en dealer – marknad tillsammans med en limit - orderbok. Vilket särskiljer denna studie tillsammans med de två algoritmerna DQN och PPO från tidigare studier. Främst har stokastisk optimering använts för liknande problem i tidigare studier. Agenterna lyckas framgångsrikt med att återskapa egenskaper hos finansiella tidsserier som återgång till medelvärdet och avsaknad av linjär autokorrelation. Agenterna lyckas också med att vinna över slumpmässiga strategier, med maximal vinst på 200%. Slutgiltigen lyckas även agenterna med att visa annan handelsdynamik som förväntas ske på en verklig marknad. Huvudsakligen: kluster av spreads, optimal hantering av aktielager och en minskning av spreads under simuleringarna. Detta visar att Reinforcement Learning med PPO eller DQN är relevanta val vid modellering av marknadens mikrostruktur.