Before revision: In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic forward investment performance processes (power, exponential and logarithmic) . We develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive control problem.
After revision: In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic forward investment performance processes (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection with ergodic and infinite horizon quadratic BSDE, and with a risk-sensitive control problem.