Munich Personal RePEc Archive
Login | Create Account

Optimal stopping in Levy models, for non-monotone discontinuous payoffs

Boyarchenko, Svetlana and Levendorskii, Sergei (2010): Optimal stopping in Levy models, for non-monotone discontinuous payoffs. Unpublished.

[img]
Preview
PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
384Kb

Abstract

We give short proofs of general theorems about optimal entry and exit problems in Levy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, and an entry problem with an embedded option to exit.

Item Type:MPRA Paper
Language:English
Keywords:optimal stopping, Levy processes, non-monotone discontinuous payoffs
Subjects:D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
ID Code:27999
Deposited By:Svetlana Boyarchenko
Deposited On:14. Jan 2011 02:40
Last Modified:14. Jan 2011 02:40
References:

[1] L. Alili, and A. Kyprianou "Some remarks on first passage of Levy process, the American put and pasting principles." Annals of Applied Probability 15 (2005), 2062-2080

[2] S. Assmusen, F. Avram, and M.R. Pistorius "Russian and American put options under exponential phase-type Levy models," Stochastic Processes and Applications, 109 (2004), 79-111.

[3] F. Avram, A.E. Kyprianou and M.R. Pistorius, "Exit problems for spectrally negative Levy processes and applications to (Canadized) Russian options", The Annals of Applied Probability, 14 (2004), 215-238

[4] Back, K. and D. Paulsen, "Open-Loop Equilibria and Perfect Competition in Option Exercise Games," Review of Financial Studies, 22:11 (2009), 4531-4552

[5] S. Boyarchenko, "Irreversible Decisions and Record-Setting News Principles", American Economic Review 94:3 (2004), pp. 557-568

[6] M. Boyarchenko and S.Z. Levendorskii, "Prices and sensitivities of barrier and first-touch digital options in Levy-driven models", International Journal of Theoretical and Applied Finance 12 (2009), pp. 1125-1170

[7] S.I. Boyarchenko and S.Z. Levendorskii, "Option pricing for truncated Levy processes", International Journal of Theoretical and Applied Finance, 3:3 (July 2000), pp. 549-552.

[8] S.I. Boyarchenko and S.Z. Levendorskii, "Perpetual American Options under Levy Processes," SIAM Journal on Control and Optimization, 40 (2002), 1663-1696.

[9] S.I. Boyarchenko and S.Z. Levendorskii, Non-Gaussian Merton-Black-Scholes theory. Singapore: World Scientific 2002.

[10] S.I. Boyarchenko and S.Z. Levendorskii, "American options: the EPV pricing model", Annals of Finance 1:3 (2005), 267-292.

[11] S.I. Boyarchenko and S.Z. Levendorskii, "General Option Exercise Rules, with Applications to Embedded Options and Monopolistic Expansion", Contributions to Theoretical Economics, 6:1 (2006), Article 2

[12] S.I. Boyarchenko and S.Z. Levendorskii, "Irreversible Decisions Under Uncertainty (Optimal Stopping Made Easy)", Springer, Berlin, 2007.

[13] S.I. Boyarchenko and S.Z. Levendorskii, "Practical guide to real options in discrete time", International Economic Review, 48:1 (2007), 275-306.

[14] S.I. Boyarchenko and S.Z. Levendorskii, \Exit Problems in Regime-Switching Models", Journ. of Mathematical Economics 44:2 (2008), 180-206

[15] S.I. Boyarchenko and S.Z. Levendorskii, "Pricing American Options in Regime-Switching Models", SIAM J Control and Optimization, 48:4 (2009), pp.1353-1375

[16] D.A. Darling, T. Ligget and H.M. Taylor, "Optimal Stopping for partial sums", Ann Math. Statistics, 43 (1972), 1363-1368.

[17] G. Deligiannidis, H. Le, and S. Utev, "Optimal Stopping for processes with independent increments, and applications", Journ. Appl. Probability, 46 (2009), 1130-1145.

[18] S. Grenadier, "Game Choices: The Intersection of Real Options and Game Theory," Risk Books, 2000

[19] S. Grenadier, "Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms," Review of Financial Studies 15:3 (2002), 691-721

[20] T.C. Johnson and M. Zervos, "The explicit solution to a sequential switching problem with non-smooth data," Stochastics: an International Journal of Probability and Stochastic Processes 82:1 (2010), 69-109

[21] A.E. Kyprianou, and B.A. Surya, "On the Novikov-Shiryaev optimal stopping problems in continuous time", Electronic Commun. Prob. 10 (2005), 146-154.

[22] A. Merhi and M. Zervos, "A model for reversible investment capacity expansion," SIAM Journal on Control and Optimization 46:3 (2007), 839-876

[23] E. Mordecki, "Optimal stopping and perpetual options for Levy processes", Finance Stoch. 6 (2002), 473-493.

[24] A.A. Novikov and A.N. Shiryaev, "On an effective case of the solution of the optimal stopping problem for random walks", Theory Prob. Appl. 49 (2005), 344-354.

[25] A.A. Novikov and A.N. Shiryaev, "On a solution of the optimal stopping problem for processes with independent increments", Stochastics 79 (2007), 393-406.

[26] G. Peskir and A. Shirayev, "Optimal Stopping and Free-Boundary Problems (Lectures in Mathematics. ETH Zurich)", Birkhauser, Basel Boston Berlin 2006

[27] F. Riedel, "Optimal stopping with multiple priors", Econometrica, 77:3 (2009), 857-908

[28] F. Riedel and Xia Su, "On Irreversible Investment," Finance and Stochastics, to appear

[29] L.C.G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales. Volume 1. Foundations, 2nd ed. John Wiley & Sons, Ltd., Chichester, 1994.

[30] M. Sirbu, and S.E. Shreve, "A two person game for pricing convertible bonds," SIAM Journal on Control and Optimization 45:4 (2006), 1508-1539

[31] Sato, Ken-Iti, Levy Processes and Infinitely Divisible Distributions. Cambridge: Cambridge University Press 1999.

[32] B.A. Surya, "An approach for solving perpetual optimal stopping problems driven by Levy processes." Stochastics, 79 (2007), 337-361.

[33] M.D. Whinston, "Exit with multiplant firms." RAND Journal of Economics, 19 (1988), 568-588.

[34] M. Zervos, "A problem of sequential entry and exit decisions combined with discretionary stopping", SIAM Journal on Control and Optimization 42:2 (2003), 397-421 2

Repository Staff Only: item control page

LMU-Logo
MPRA is a RePEc service hosted by
the Munich University Library in Germany.