Dynamic Portfolio Selection Under Monotone Additive Statistics in a Stochastic Volatility Model

Monotone additive statistics are preference representations satisfying the monotonicity and additivity properties. These statistics have been proven to be represented by weighted averages of certainty equivalents under exponential utility functions with different risk aversion degrees and employed in various financial and economic contexts. We study a dynamic portfolio selection problem in which an agent trades a risk‐free asset and a risky stock with stochastic volatility to optimize her investment performance measured by a monotone additive statistic of her terminal wealth or log investment return. Because monotone additive statistics, when applied to dynamic decision problems, can lead to time inconsistency, we consider equilibrium strategies for our portfolio selection problem. We derive these strategies by proving the solvability of two associated systems of ordinary differential equations.