Optimal investments for robust utility functional in complete market models

Mathematics of Operations Research

Volumn 30, Issue 3, 2005, Pages 750-764

  Schied, Alexander ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Huber Strassen theory; Knightian uncertainty; Least favorable measure; Robust Savage representation; Robust utility functional; Uncertain drift; Utility maximization

Indexed keywords

INDUSTRIAL ECONOMICS; MARKETING; MATHEMATICAL MODELS; OPERATIONS RESEARCH; PROBABILITY; ROBUSTNESS (CONTROL SYSTEMS);

HUBER-STRASSEN THEORY; KNIGHTIAN UNCERTAINTY; LEAST FAVORABLE MEASURE; ROBUST SAVAGE REPRESENTATION; ROBUST UTILITY FUNCTIONAL; UNCERTAIN DRIFT; UTILITY MAXIMIZATION;

INVESTMENTS;

EID: 31144452786     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1040.0138     Document Type: Article

References (30)

1. Augustin, T. 2002. Neyman-Pearson testing under interval probability by globally least favorable pairs reviewing Huber-Strassen theory and extending it to general interval probability, imprecise probability models and their applications. J. Statist. Planning Inference 105 149-173.
2. Baudoin, F. 2002. Conditioned stochastic differential equations: theory, examples and application to finance. Stochastic Process. Appl. 100 109-145.
3. Bednarski, T. 1981. On solutions of minimax test problems for special capacities. Z. Wahrsch. Verw. Gebiete 58 397-405.
4. Bednarski, T. 1982. Binary experiments, minimax tests and 2-alternating capacities. Ann. Statist. 10 226-232.
5. Chen, Z., A. Sulem. 2001. An integral representation theorem of g-expectations. INRIA Rapport de Recherche No. 4284,
6. Choquet, G. 1953/1954. Theory of capacities. Ann. Inst. Fourier 5 131-292.
7. Cont, R. 2004. Model uncertainty and its impact on the pricing of derivative instruments. Preprint, École Polytechnique de Paris,
8. Delbaen, F. 2000. Coherent risk measures. Lecture notes, Scuola Normale di Pisa, Pisa, Italy.
9. El Karoui, N., M. Jeanblanc-Picqué, S. Shreve. 1998. Robustness of the Black and Scholes formula. Math. Finance 8 93-126.
10. Föllmer, H., A. Schied. 2004. Stochastic Finance: An Introduction in Discrete Time, 2nd ed. De Gruyter Studies in Mathematics, No. 27. Berlin, Germany.
11. Gilboa, I. 1987. Expected utility with purely subjective non-additive probabilities. J. Math. Econom. 16 65-88.
12. Gilboa, I., D. Schmeidler. 1989. Maxmin expected utility with non-unique prior. J. Math. Econom. 18 141-153.
13. Gundel, A. 2003. Robust utility maximization in complete and incomplete market models. Preprint, Humboldt-Universität zu Berlin, Berlin, Germany.
14. Hajek, B. 1985. Mean stochastic comparison of diffusions. Z. Wahrsch. Verw. Gebiete 68 315-329.
15. Hobson, D. 1998. Volatility mis-specification, option pricing and super-replication via coupling. Ann. Appl. Probab. 8 193-205.
16. Huber, P. 1981. Robust Statistics. Wiley Series in Probability and Mathematical Statistics. John Wiley and Sons, New York.
17. Huber, P., V. Strassen. 1973, 1974. Minimax tests and the Neyman-Pearson lemma for capacities. Ann. Statist. 1 251-263. Correction. Ann. Statist. 2 223-224.
18. Janson, S., J. Tysk. 2003. Volatility time and properties of option prices. Ann. Appl. Probab. 13 890-913.
19. Karatzas, I., S. Shreve. 1998. Methods of Mathematical Finance. Applications of Mathematics. Springer, Berlin, Germany.
20. Kramkov, D., W. Schachermayer. 1999. The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9(3) 904-950.
21. Kramkov, D., W. Schachermayer. 2003. Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 13 1504-1516.
22. Kusuoka, S. 2001. On law invariant coherent risk measures. Adv. Math. Econom. 3 83-95.
23. Lembcke, J. 1988. The necessity of strongly subadditive capacities for Neyman-Pearson minimax tests. Monatsh. Math. 105 113-126.
24. Peng, S. 1997. Backward SDE and related g-expectation. Backward Stochastic Differential Equations (Paris, 1995-1996), Pitman Research Notes Mathematics Series, No. 364, Longman, Harlow, UK, 141-159.
25. Schachermayer, W. 2001. Optimal investment in incomplete financial markets. Proc. First World Congress of the Bachelier Soc., Paris 2000. Springer-Verlag, Berlin, Germany.
26. Schied, A. 2004. On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals. Ann. Appl. Probab. 14 1398-1423.
27. Schied, A., C.-T. Wu. 2004. Duality theory for optimal investments under model uncertainty. Preprint, Technische Universität Berlin, Berlin, Germany.
28. Schmeidler, D. 1989. Subjective probability and expected utility without additivity. Econometrica 57 571-587.
29. Skiadas, C. 2003. Robust control and recursive utility. Finance Stoch. 7 475-489.
30. Yaari, M. 1987. The dual theory of choice under risk. Econometrica 55 95-115.