Incorporating positions into asset pricing models with order-based strategies

The paper addresses the problem of agent-based asset pricing models with order-based strategies that the implied positions of the agents remain indeterminate. To overcome this inconsistency, two easily applicable risk aversion mechanisms are proposed which modify the original actions of a market maker and the speculative agents, respectively. Here the concepts are incorporated into the classical Beja–Goldman model. For the deterministic version of the thus enhanced model a four-dimensional mathematical stability analysis is provided. In a stochastic version it is demonstrated that jointly the mechanisms are indeed able to keep the agents’ positions within bounds, provided the corresponding risk aversion coefficients are neither too low nor too high. A similar result holds for the misalignment of the market price. We wish to thank two anonymous referees for their observations and detailed comments. Financial support from EU STREP ComplexMarkets, contract number 516446, is gratefully acknowledged.