Boyarchenko, Svetlana and Levendorskii, Sergei (2010): Optimal stopping in Levy models, for nonmonotone discontinuous payoffs.

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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 nonmonotone. 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 

Original Title:  Optimal stopping in Levy models, for nonmonotone discontinuous payoffs 
Language:  English 
Keywords:  optimal stopping, Levy processes, nonmonotone discontinuous payoffs 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis 
Item ID:  27999 
Depositing User:  Svetlana Boyarchenko 
Date Deposited:  14. Jan 2011 01:40 
Last Modified:  12. Feb 2013 21:32 
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), 20622080 [2] S. Assmusen, F. Avram, and M.R. Pistorius "Russian and American put options under exponential phasetype Levy models," Stochastic Processes and Applications, 109 (2004), 79111. [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), 215238 [4] Back, K. and D. Paulsen, "OpenLoop Equilibria and Perfect Competition in Option Exercise Games," Review of Financial Studies, 22:11 (2009), 45314552 [5] S. Boyarchenko, "Irreversible Decisions and RecordSetting News Principles", American Economic Review 94:3 (2004), pp. 557568 [6] M. Boyarchenko and S.Z. Levendorskii, "Prices and sensitivities of barrier and firsttouch digital options in Levydriven models", International Journal of Theoretical and Applied Finance 12 (2009), pp. 11251170 [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. 549552. [8] S.I. Boyarchenko and S.Z. Levendorskii, "Perpetual American Options under Levy Processes," SIAM Journal on Control and Optimization, 40 (2002), 16631696. [9] S.I. Boyarchenko and S.Z. Levendorskii, NonGaussian MertonBlackScholes 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), 267292. [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), 275306. [14] S.I. Boyarchenko and S.Z. Levendorskii, \Exit Problems in RegimeSwitching Models", Journ. of Mathematical Economics 44:2 (2008), 180206 [15] S.I. Boyarchenko and S.Z. Levendorskii, "Pricing American Options in RegimeSwitching Models", SIAM J Control and Optimization, 48:4 (2009), pp.13531375 [16] D.A. Darling, T. Ligget and H.M. Taylor, "Optimal Stopping for partial sums", Ann Math. Statistics, 43 (1972), 13631368. [17] G. Deligiannidis, H. Le, and S. Utev, "Optimal Stopping for processes with independent increments, and applications", Journ. Appl. Probability, 46 (2009), 11301145. [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), 691721 [20] T.C. Johnson and M. Zervos, "The explicit solution to a sequential switching problem with nonsmooth data," Stochastics: an International Journal of Probability and Stochastic Processes 82:1 (2010), 69109 [21] A.E. Kyprianou, and B.A. Surya, "On the NovikovShiryaev optimal stopping problems in continuous time", Electronic Commun. Prob. 10 (2005), 146154. [22] A. Merhi and M. Zervos, "A model for reversible investment capacity expansion," SIAM Journal on Control and Optimization 46:3 (2007), 839876 [23] E. Mordecki, "Optimal stopping and perpetual options for Levy processes", Finance Stoch. 6 (2002), 473493. [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), 344354. [25] A.A. Novikov and A.N. Shiryaev, "On a solution of the optimal stopping problem for processes with independent increments", Stochastics 79 (2007), 393406. [26] G. Peskir and A. Shirayev, "Optimal Stopping and FreeBoundary Problems (Lectures in Mathematics. ETH Zurich)", Birkhauser, Basel Boston Berlin 2006 [27] F. Riedel, "Optimal stopping with multiple priors", Econometrica, 77:3 (2009), 857908 [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), 15081539 [31] Sato, KenIti, 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), 337361. [33] M.D. Whinston, "Exit with multiplant firms." RAND Journal of Economics, 19 (1988), 568588. [34] M. Zervos, "A problem of sequential entry and exit decisions combined with discretionary stopping", SIAM Journal on Control and Optimization 42:2 (2003), 397421 2 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/27999 