A markov-modulated stochastic control problem with optimal multiple stopping with application to finance

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2010, Pages 559-566

  Leung, Tim Siu Tang ^a  

^a Johns Hopkins University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; STOCHASTIC SYSTEMS; VARIATIONAL TECHNIQUES;

AMERICAN OPTIONS; ASSET PRICES; INCOMPLETE MARKETS; MULTIPLE STOPPING; RELATIVE-ENTROPY MINIMIZATION; STOCHASTIC CONTROL; SYSTEM OF VARIATIONAL INEQUALITIES; UTILITY MAXIMIZATIONS;

STOCHASTIC CONTROL SYSTEMS;

EID: 79953132485     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2010.5717052     Document Type: Conference Paper

References (19)

1. T. Leung and R. Sircar, "Accounting for risk aversion, vesting, job termination risk and multiple exercises in valuation of employee stock options," Mathematical Finance, vol. 19, no. 1, pp. 99-128, January 2009.
2. M. Davis, "Pricing weather derivatives by marginal value," Quantitative Finance, vol. 1, pp. 1-4, 2001.
3. -, "Option pricing in incomplete markets," in Mathematics of Derivatives Securities, M. Dempster and S. Pliska, Eds. Cambridge University Press, 1997, pp. 227-254.
4. A. Oberman and T. Zariphopoulou, "Pricing early exercise contracts in incomplete markets," Computational Management Science, vol. 1, pp. 75-107, 2003.
5. X. Guo and Q. Zhang, "Closed-form solutions for perpetual american put options with regime switching," SIAM Journal on Applied Mathematics, vol. 64, no. 6, pp. 2034-2049, 2004.
6. R. J. Elliot, L. Chan, and T. K. Siu, "Option pricing and esscher transform under regime switching," Annals of Finance, vol. 1, pp. 423-432, 2005.
7. M. Fritelli, "The minimal entropy martingale measure and the valuation problem in incomplete markets," Mathematical Finance, vol. 10, pp. 39-52, 2000.
8. F. Delbaen, P. Grandits, T. Rheinländer, D. Samperi, M. Schweizer, and C. Stricker, "Exponential hedging and entropic penalties," Math- ematical Finance, vol. 12, pp. 99-123, 2002.
9. I. Karatzas and S. Shreve, Methods of Mathematical Finance. Springer, 1998.
10. R. Merton, "Lifetime portfolio selection under uncertainty: the continuous time model," Review of Economic Studies, vol. 51, pp. 247-257, 1969.
11. W. H. Fleming and S. Sheu, "Optimal long term growth rate of expected utility of wealth," Ann. Appl. Probab., vol. 9, no. 3, pp. 871-903, 1999.
12. T. Leung and R. Sircar, "Exponential hedging with optimal stopping and application to ESO valuation," SIAM Journal of Control and Optimization, vol. 48, no. 3, pp. 1422-1451, 2009.
13. T. Leung, "The impacts of risk aversion and market regimes on dynamic hedging and multiple exercises of American options," 2010, working paper, Johns Hopkins University.
14. P. Wilmott, S. Howison, and J. Dewynne, The Mathematics of Financial Derivatives. Cambridge University Press, 1995.
15. H. Föllmer and D. Sondermann, "Hedging of non-redundant contingent claims," in Contribution to Mathematical Economics: In Honor of Gerard Debreu, W. Hildenbrand and A. Mas-Colell, Eds. Amsterdam, North-Holland, 1986.
16. L. Rogers and D. Williams, Diffusions, Markov Processes and Martingales, 2nd ed. Cambridge University Press, UK, 2000.
17. P. Grandits and T. Rheinländer, "On the minimal entropy martingale measure," Annals of Probability, vol. 30, pp. 1003-1038, 2002.
18. Y. Kabanov and C. Stricker, "On the optimal portfolio for the exponential utility maximization: Remarks to the six-author paper," Mathematical Finance, vol. 12, pp. 125-134, 2002.
19. I. Karatzas and S. Kou, "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, vol. 2, pp. 215-258, 1998.