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In an incomplete market, with incompleteness stemming from stochastic factorsimperfectly correlated with the underlying stocks, we derive representations ofhomothetic (power, exponential and logarithmic) forward performance processesin factor-form using ergodic BSDE. We also develop a connection between theforward processes and infinite horizon BSDE, and, moreover, with risk-sensitiveoptimization. In addition, we develop a connection, for large time horizons,with a family of classical homothetic value function processes with randomendowments.

Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE