Before revision:  We develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive control problem. We also develop a connection, for large trading horizons, with a family of traditional homothetic value function processes  .
After revision:  We develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive optimization. In addition, we develop a connection, for large trading horizons, with a family of traditional homothetic value function processes .