Sensitivity analysis of utility-based prices and risk-tolerance wealth processes

Annals of Applied Probability

Volumn 16, Issue 4, 2006, Pages 2140-2194

  Kramkov, Dmitry ^a   Sîrbu, Mihai ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

Contingent claim; Hedging; Incomplete markets; Random endowment; Risk aversion; Risk tolerance; Stochastic dominance; Utility maximization; Utility based valuation

Indexed keywords

EID: 33750503695     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051606000000529     Document Type: Article

References (16)

1. DAVIS, M. H. A. (1997). Option pricing in incomplete markets. In Mathematics of Derivative Securities (M. A. H. Dempster and S. R. Pliska, eds.) 216-226. Cambridge Univ. Press. MR1491376
2. DELBAEN, F. and SCHACHERMAYER, W. (1994). A general version of the fundamental theorem of asset pricing. Math. Ann. 300 463-520. MR1304434
3. DELBAEN, F. and SCHACHERMAYER, W. (1997). The Banach space of workable contingent claims in arbitrage theory. Ann. Inst. H. Poincaré Probab. Statist. 33 113-144. MR1440258
4. DELBAEN, F. and SCHACHERMAYER, W. (1998). The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann. 312 215-250. MR1671792
5. FÖLLMER, H. and SCHIED, A. (2004). Stochastic Finance: An Introduction in Discrete Time, 2nd ed. de Gruyter, Berlin. MR2169807
6. HENDERSON, V. (2002). Valuation of claims on nontraded assets using utility maximization. Math. Finance 12 351-373. MR1926237
7. HENDERSON, V. and HOBSON, D. G. (2002). Real options with constant relative risk aversion. J. Econom. Dynam. Control 21 329-355. MR1930735
8. HUGONNIER, J. and KRAMKOV, D. (2004). Optimal investment with random endowments in incomplete markets. Ann. Appl. Probab. 14 845-864. MR2052905
9. HUGONNIER, J., KRAMKOV, D. and SCHACHERMAYER, W. (2005). On utility-based pricing of contingent claims in incomplete markets. Math. Finance 15 203-212. MR2132189
10. ILHAN, A., JONSSON, M. and SIRCAR, R. (2005). Optimal investment with derivative securities. Finance Stock. 9 585-595. MR2212897
11. JACKA, S. D. (1992). A martingale representation result and an application to incomplete financial markets. Math. Finance 2 239-250.
12. KALLSEN, J. (2002). Derivative pricing based on local utility maximization. Finance Stoch. 6 115-140. MR1885586
13. KRAMKOV, D. and SCHACHERMAYER, W. (1999). The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9 904-950. MR1722287
14. KRAMKOV, D. and SÎRBU, M. (2006). On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 16 1352-1384.
15. MUSIELA, M. and ZARIPHOPOULOU, T. (2004). An example of indifference prices under exponential preferences. Finance Stoch. 8 229-239. MR2048829
16. RUBINSTEIN, M. (1976). The valuation of uncertain income streams and the pricing of options. Bell J. Econom. 7 407-425. MR0679720