Karatzas et al. (SIAM J. Control Optim. 29:707-730, 1991) ensure the existence of the expected utility maximizer for investors with constant relative risk aversion coefficients less than one. In this note, we explain a simple trick that allows us to use this result to provide the existence of utility maximizers for arbitrary coefficients of relative risk aversion. The simplicity of our approach is to be contrasted with the general existence result provided in Kramkov and Schachermayer (Ann. Appl. Probab. 9:904-950, 1999).
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- CRRA preferences
- Change of measure
- Convex duality
- Incomplete markets