The prospect theory of Kahneman and Tversky (in Econometrica 47(2), 263–291, 1979) and the cumulative prospect theory of Tversky and Kahneman (in J. Risk uncertainty 5, 297–323, 1992) are descriptive models for decision making that summarize several violations of the expected utility theory. This paper gives a survey of applications of prospect theory to the portfolio choice problem and the implications for asset pricing. We demonstrate that prospect theory (and similarly cumulative prospect theory) has to be re-modelled if one wants to apply it to portfolio selection. We suggest replacing the piecewise power value function of Tversky and Kahneman (in J. Risk uncertainty 5, 297–323, 1992) with a piecewise negative exponential value function. This latter functional form is still compatible with laboratory experiments but it has the following advantages over and above Tversky and Kahneman’s piecewise power function:
1. The Bernoulli Paradox does not arise for lotteries with finite expected value.
2. No infinite leverage/robustness problem arises.
3. CAPM-equilibria with heterogeneous investors and prospect utility do exist.
4. It is able to simultaneously resolve the following asset pricing puzzles: the equity premium, the value and the size puzzle.
In contrast to the piecewise power value function it is able to explain the disposition effect.
Resolving these problems of prospect theory we show how it can be combined with mean–variance portfolio theory.