1. Failure of the smooth pasting principle was demostrated for the first time in

• S.I.Boyarchenko, S.Z.Levendorskiĭ,, Perpetual American options under Lévy processes, SIAM Journal on Control and Optimization, 40:6 (2002), 1663--1696   pdf file

2. New approach to optimal stopping problems based on the operator form of the Wiener-Hopf factorization and interpretation of the factors as expected present value operators (EPV-operators) under supremum and infimum processes. General optimal exercise rules for general payoff functions and wide classes of Lévy processes, and in regime-switching models. Applications to several problems in economics. The results are obtained in dicrete and continuous time and/or space.

• S. Boyarchenko and S. Levendorskiĭ, Irreversible Decisions under Uncertainty (Optimal Stopping made Easy), Springer-Verlag, Berlin, 2007, xvi+283 pp.
• S. Boyarchenko and S. Levendorskiĭ, Non-Gaussian Merton-Black-Scholes theory, World Scientific, Singapore, 2002, xxi+398 pp.
• S. Boyarchenko and S. Levendorskiĭ, Optimal stopping made easy, Journ. of Mathematical Economics, 43:2 (2007), pp. 201-217 http://ssrn.com/abstract=610621
• S. Boyarchenko and S. Levendorskiĭ, General option exercise rules, with applications to embedded options and monopolistic expansion, Contributions to Theoretical Economics, 6:1, Article 2 (2006) http://ssrn.com/abstract=838624
• S. Boyarchenko and S. Levendorskiĭ, The practical guide to real options in discrete time,  International Economic Review   48:1 (2007), 275--306.  http://ssrn.com/abstract=642262
• S. Boyarchenko and S. Levendorskiĭ,  American options: the EPV pricing model , Annals of Finance  (2005), 1, 267--292. http://ssrn.com/abstract=547863
• S. Boyarchenko and S. Levendorskiĭ,     Pricing of perpetual Bermudan options, Quantitative Finance, 2 (2002), 422-432  http://www.eco.utexas.edu/~leven/bermud3.pdf
• S.Z. Levendorskiĭ, S.I. Boyarchenko, Investment under Uncertainty when Shocks are Non-Gaussian, Preprint 98/8, Institut für Mathematik, Uni Potsdam, 1998. PostScript File (zipped)

3. Applications to regime-switching models.

• Svetlana Boyarchenko, Sergei Levendorskiĭ, Exit Problems in Regime-Switching Models, Journ. of Mathematical Economics 44:2 (2008), 180-206 
• Svetlana Boyarchenko, Sergei Levendorskiĭ, Perpetual American Options in Regime-Switching Models (September 5, 2006)  http://ssrn.com/abstract=928474

4. Mean-reverting models.

• Perpetual American Options and Real Options under Mean-Reverting Processes (2005) http://ssrn.com/abstract=714321
• S. Boyarchenko and S. Levendorskiĭ, Irreversible Decisions under Uncertainty (Optimal Stopping made Easy), Springer-Verlag, Berlin, 2007, xvi+283 pp.