Mathematical modelling of diffusion approximation of birth & death ebook download pdf
Starting with the work of Kirman in the year 1993, herding models for financial markets are investigated in a variety of papers. In this article we concentrate on the model described in. They consider a nancial market with a xed number of agents N . These agents are either optimistic or pessimistic about the future market behaviour. In this paper we take a mathematical look on the process of optimistic agents for which the standard mathematical model is modelled as a birth and death process. A death stands for an optimistic agent who chances his opinion and a birth stands for an pessimistic agent who gets optimistic. This swing of opinion can happen due to two factors. The rest is that the agent chances his opinion without inuence from his peers. For a change due to group pressure it is important to assume that the agents are connected in a network and communicate with each other. Possible underlying network structures are considered in. We refer to the cited papers for detailed information on the economic background.