We analyze the portfolio choice problem of investors who maximize rank dependent utility in a single-period complete market. We propose a new
notion of less risk taking: choosing optimal terminal wealth that pays off more in bad states and less in good states of the economy. We prove that investors with a less risk averse preference relation in general choose more risky terminal wealth, receiving a risk premium in return for accepting conditional-zero-mean noise (more risk). Such general comparative static results do not hold for portfolio weights, which we demonstrate with a counter-example in a continuous-time model. This in turn suggests that our notion of less risk taking is more meaningful than the traditional notion based on holding less stocks.
This is a joint work with Xuedong He and Roy Kouwenberg.
- Mathematical Finance Internal Seminar