On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals

Annals of Applied Probability

Volumn 14, Issue 3, 2004, Pages 1398-1423

  Schied, Alexander ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Generalized moment problem; Law invariant risk measure; Neyman Pearson problem; Optimal contingent claim; Robust utility functional

Indexed keywords

EID: 25644448592     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051604000000341     Document Type: Article

References (25)

1. ARTZNER, P., DELBAEN, F., EBER, J.-M. and HEATH, D. (1999). Coherent measures of risk. Math. Finance 9 203-228.
2. BEDNARSKI, T. (1981). On solutions of minimax test problems for special capacities. Z. Wahrsch. Verw. Gebiete 58 397-405.
3. CVITANIĆ, J. (2000). Minimizing expected loss of hedging in incomplete and constrained markets. SIAM J. Control Optim. 38 1050-1066.
4. CVITANIĆ, J. and KARATZAS, I. (2001). Generalized Neyman-Pearson lemma via convex duality. Bernoulli 7 79-97.
5. DANA, R.-A. and CARLIER, G. (2002). Core of convex distortions of a probability on an non atomic space. Preprint, Ceremade, Univ. Paris-Dauphine.
6. DELBAEN, F. (2002). Coherent measures of risk on general probability spaces. In Advances in Finance and Stochastics. Essays in Honour of Dieter Sondermann (K. Sandmann and P. J. Schönbucher, eds.) 1-37. Springer, Berlin.
7. DELBAEN, F. (2000). Coherent Risk Measures. Scuola Normale Superiore, Classe di Scienze, Pisa.
8. DENNEBERG, D. (1994). Non-additive Measure and Integral. Kluwer Academic, Dordrecht.
9. FÖLLMER, H. and LEUKERT, P. (1999). Quantile hedging. Finance Stoch. 3 251-273.
10. FÖLLMER, H. and LEUKERT, P. (2000). Efficient hedging: Cost versus shortfall risk. Finance Stoch. 4 117-146.
11. FÖLLMER, H. and SCHIED, A. (2002). Convex measures of risk and trading constraints. Finance Stoch. 6.
12. FÖLLMER, H. and SCHIED, A. (2002). Robust representation of convex measures of risk. In Advances in Finance and Stochastics. Essays in Honour of Dieter Sondermann (K. Sandmann and P. J. Schönbucher, eds.) 39-56. Springer, Berlin.
13. FÖLLMER, H. and SCHIED, A. (2002). Stochastic Finance: An Introduction in Discrete Time. Springer, Berlin.
14. GILBOA, I. and SCHMEIDLER, D. (1989). Maxmin expected utility with non-unique prior. J. Math. Econ. 18 141-153.
15. HUBER, P. (1981). Robust Statistics. Wiley, New York.
16. HUBER, P. and STRASSEN, V. (1973). Minimax tests and the Neyman-Pearson lemma for capacities. Ann. Statist. 1 251-263.
17. KIRCH, M. (2002). Maximin-optimal tests and least favorable pairs for concave power functions. Preprint, TU Wien.
18. KIRCH, M. (2002). Efficient hedging in incomplete markets under model uncertainty. Preprint, TU Wien.
19. KULLDORFF, M. (1993). Optimal control of favorable games with a time limit. SIAM J. Control Optim. 31 52-69.
20. KUSUOKA, S. (2001). On law invariant coherent risk measures. Adv. Math. Econ. 3 83-95.
21. ÖSTERREICHER, F. (1978). On the construction of least favourable pairs of distributions. Z. Wahrsch. Verw. Gebiete 43 49-55.
22. PHAM, H. (2002). Minimizing shortfall risk and applications to finance and insurance problems. Ann. Appl. Probab. 12 143-172.
23. RIEDER, H. (1977). Least favourable pairs for special capacities. Ann. Statist. 5 909-921.
24. VON WEIZSÄCKER, H. and WINKLER, G. (1979). Integral representations in the set of solutions of a generalized moment problem. Math. Ann. 246 23-32.
25. WINKLER, G. (1988). Extreme points of moment sets. Math. Oper. Res. 13581-587.