| Abstract: |
| The monotone additive statistic is a preference representation satisfying the monotonicity and additivity properties. This statistic has been proven to be represented by a weighted average 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 the monotone additive statistic of her terminal wealth or log investment return. We find that the monotone additive statistic, when applied to dynamic decision problems, can lead to time inconsistency. We thus consider equilibrium strategies for our portfolio selection problem and derive these strategies by proving the solvability of two associated systems of ordinary differential equations. |
|