# Prospect Theory and Optimal Risky Choices with Goals

- Jana Jarecki, Economic Psychology, University of Basel, Bsel, Switzerland
- Jörg Rieskamp, Economic Psychology, University of Basel, Basel, Switzerland

**Abstract**Decision making under risk is often studied as a preferential choice governed by stable individual personality characteristics, but risky choice can also be viewed as a dynamic problem of resource accumulation to survive. When decision makers aim to reach a particular goal in limited time, such as “earn at least $100 in five choices,” risky choice becomes a non-trivial planning problem. This problem has an optimal solution that can differ from immediate expected-value maximization. We studied the optimality of risky choices under such minimum goal requirements experimentally and find that the observed choices under goals approximate the optimal solution. However, because the optimal model is very complex, we examine if simpler models can predict people’s choices better. We test an extended version of prospect theory, assuming a dynamic reference point that depends on the distance to the goal. This “dynamic prospect theory” was better than the alternative model in describing people’s decisions (i.e., for 63% of the participants, it was the best model). Our findings show that humans can excel in a highly complex, dynamic, risky choice problem and that a dynamic version of prospect theory provides one possible explanation for how people decide under risk when long-term goals matter.