<p>This paper pioneers behavioral portfolio decisions as per prospect theory under a stochastic volatility setting that is exemplified by the use of an affine GARCH model. We derive a closed-form representation for the allocation towards the risky asset based on a delta replication of the optimal terminal wealth under a given risk-neutral measure. Our proposed methodology can be viewed as an adaptation of the Martingale method, combining (1) a static maximization for a given pricing kernel to derive the best terminal wealth and (2) delta-hedging to create a replicating portfolio. Our results demonstrate the remarkable impact of stochastic volatility on behavioral portfolio allocations and their performance for a variety of parametrizations for the investors’ risk aversion and risk-seeking preferences, reference level, and investment horizon. Moreover, we find that neglecting stochastic volatility in the decision process can lead to significant expected utility losses. In particular, the certainty equivalence from considering a GARCH model could be 20% larger than from assuming a constant volatility setting for standard market conditions and investors.</p>