Risk aversion asymptotics for power utility maximization

Probability Theory and Related Fields

Volumn 152, Issue 3-4, 2012, Pages 703-749

  Nutz, Marcel ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

BSDE; Opportunity process; Power utility; Risk aversion asymptotics

Indexed keywords

EID: 84858149014     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-010-0334-3     Document Type: Article

References (31)

1. Ansel, J. P., Stricker, C.: Décomposition de Kunita-Watanabe. In: Séminaire de Probabilités XXVII. Lecture Notes in Math., vol. 1557, pp. 30-32. Springer, Berlin (1993).
2. Becherer D.: Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging. Ann. Appl. Probab. 16(4), 2027-2054 (2006).
3. Biagini S., Frittelli M.: Utility maximization in incomplete markets for unbounded processes. Finance Stoch. 9(4), 493-517 (2005).
4. Biagini S., Frittelli M.: The supermartingale property of the optimal wealth process for general semimartingales. Finance Stoch. 11(2), 253-266 (2007).
5. Carassus L., Rásonyi M.: Convergence of utility indifference prices to the superreplication price. Math. Methods Oper. Res. 64(1), 145-154 (2006).
6. Delbaen F., Monat P., Schachermayer W., Schweizer M., Stricker C.: Weighted norm inequalities and hedging in incomplete markets. Finance Stoch. 1(3), 181-227 (1997).
7. Delbaen F., Schachermayer W.: The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann. 312, 215-250 (1998).
8. Dellacherie C., Meyer P. A.: Probabilities and Potential B. North Holland, Amsterdam (1982).
9. Émery, M.: Une topologie sur l'espace des semimartingales. In: Séminaire de Probabilités XIII. Lecture Notes in Math., vol. 721, pp. 260-280. Springer, Berlin (1979).
10. Frei, C., Schweizer, M.: Exponential utility indifference valuation in a general semimartingale model. In: Delbaen, F., Rásonyi, M., Stricker, C. (eds) Optimality and Risk-Modern Trends in Mathematical Finance. The Kabanov Festschrift, pp. 49-86. Springer, Berlin (2009).
11. Goll T., Kallsen J.: Optimal portfolios for logarithmic utility. Stoch. Process. Appl. 89(1), 31-48 (2000).
12. Goll T., Kallsen J.: A complete explicit solution to the log-optimal portfolio problem. Ann. Appl. Probab. 13(2), 774-799 (2003).
13. Gollier C.: The Economics of Risk and Time. MIT Press, Cambridge (2001).
14. Grandits P., Rheinländer T.: On the minimal entropy martingale measure. Ann. Probab. 30(3), 1003-1038 (2002).
15. Grandits P., Summer C.: Risk averse asymptotics and the optional decomposition. Theory Probab. Appl. 51(2), 325-334 (2007).
16. Grasselli M.: A stability result for the HARA class with stochastic interest rates. Insurance Math. Econ. 33(3), 611-627 (2003).
17. Jacod J., Shiryaev A. N.: Limit Theorems for Stochastic Processes, 2nd edn. Springer, Berlin (2003).
18. Jouini E., Napp C.: Convergence of utility functions and convergence of optimal strategies. Finance Stoch. 8(1), 133-144 (2004).
19. Kabanov Yu., Stricker C.: On the optimal portfolio for the exponential utility maximization: Remarks to the six-author paper. Math. Finance. 12, 125-134 (2002).
20. Karatzas I., Žitković G.: Optimal consumption from investment and random endowment in incomplete semimartingale markets. Ann. Probab. 31(4), 1821-1858 (2003).
21. Kardaras, C., Žitković, G.: Stability of the utility maximization problem with random endowment in incomplete markets. Math. Finance (To appear).
22. Kobylanski M.: Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab. 28(2), 558-602 (2000).
23. Larsen K.: Continuity of utility-maximization with respect to preferences. Math. Finance 19(2), 237-250 (2009).
24. Mania M., Schweizer M.: Dynamic exponential utility indifference valuation. Ann. Appl. Probab. 15(3), 2113-2143 (2005).
25. Mania M., Tevzadze R.: A unified characterization of the q-optimal and minimal entropy martingale measures. Georgian Math. J. 10(2), 289-310 (2003).
26. Nutz, M.: The Bellman equation for power utility maximization with semimartingales. Preprint arXiv: 0912. 1883v1 (2009).
27. Nutz M.: The opportunity process for optimal consumption and investment with power utility. Math. Financ. Econ. 3(3), 139-159 (2010).
28. Protter P.: An extension of Kazamaki's results on BMO differentials. Ann. Probab. 8(6), 1107-1118 (1980).
29. Santacroce M.: On the convergence of the p-optimal martingale measures to the minimal entropy martingale measure. Stoch. Anal. Appl. 23(1), 31-54 (2005).
30. Schachermayer W.: Optimal investment in incomplete markets when wealth may become negative. Ann. Appl. Probab. 11(3), 694-734 (2001).
31. Schweizer M.: On the minimal martingale measure and the Föllmer-Schweizer decomposition. Stoch. Anal. Appl. 13, 573-599 (1995).