An economic premium principle in a multiperiod economy

This paper considers a multiperiod economic equilibrium model for deriving the economic premium principle of Bühlmann [Astin Bull. 11 (1980) 52–60; Astin Bull. 14 (1983) 13–21]. To do this, we construct a consumption/portfolio model in which each agent is characterized by his/her utility function and income and seeks to invest his/her wealth in both insurance as well as a financial market so as to maximize the expected, discounted total utility from consumption. The state price density in equilibrium is obtained in terms of the Arrow–Pratt index of absolute risk aversion for the representative agent. As special cases, power and exponential utility functions are examined, and some comparative statics results are derived.