Utility Functions with Parameters Depending on Initial Wealth

Conventional one-period utility functions in economics assume that initial wealth only enters preferences through the definition of final wealth. As a consequence, those utility functions most utilised (i.e. exponential and quadratic) have implausible risk characteristics. The authors characterise a new class of utility functions whose parameters depend upon initial wealth. Several desirable results are obtained. In particular, investors with quadratic and exponential utility functions can have decreasing risk aversion and will increase their share of the risky asset as they get wealthier. Additionally, the authors show how making parameters depend on initial wealth extends the class of functions which give two- fund separation and can convert the traditional principal-agent problem to one which accounts for observed behaviour of asset managers and pension funds.