We study the Merton portfolio optimization problem in the presence of stochastic volatility using asymptotic approximations when the volatility process is characterized by its time scales of fluctuation. This approach is tractable because it treats the incomplete markets problem as a...

Using elements from the theory of ergodic backward stochastic differential equations (BSDE), we study the behavior of forward entropic risk measures. We provide their general representation results (via both BSDE and convex duality) and examine their behavior for risk positions of long...

In an incomplete market, with incompleteness stemming from stochas- tic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) for- ward performance processes in factor-form using ergodic BSDE. We also develop a...