Risk propensity and proportion of investment for agents using power utility functions

摘要

The main goal of this article is to investigate the relationship between agent's utility function of wealth and the proportion of investment of the agent in investment models based on a multiplicative stochastic process. Multiplicative stochastic processes are of special interest because of its property to generate power laws distributions which resemble real wealth distributions. We discuss a power utility function that can be used by agents to describe their proportion of investment in terms of relative risk. Finally, we show the different relationships between the relative risk premium and the proportion of investment for different risk-propensity types (risk-averse, risk-neutral and risk-seeking). This characterization of the risk-propensity of an agent in terms of proportion of investment can be used to ease the task of modelling agent's attitude towards risk together with an utility function of wealth.