- Thesis:
- Master in Mathematics
- Author:
- Jannik Westermann
- Title:
- On monotone additive statistics
- Supervisors:
- Jan JOHANNES
- Abstract:
- A functional Φ : L → R on a set of random variables is a monotone additive statistic if it obeys some axioms about specific decision habits of economic agents. One particular aspect modelled with this framework is invariance to independent background risk. The characterization of monotone additive statistics depends on which set of random variables L is used to model background risk. Ensuring invariance to any sort of independent bounded background risk results in a characterization by Mu, Pomatto, Strack and Tamuz (2024). In this thesis I present their proof and result. Further, I present how the authors apply this theory to time lotteries. Finally, I discuss how the characterization changes when only some discrete independent background risk is taken into consideration.
- Reference:
- X. Mu, L. Pomatto, P. Strack, and O. Tamuz, Monotone additive statistics, Econometrica 92 (2024), no. 4, 995–1031.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |