Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups

Gihman, 1972 Taylor, 1975, A stopped Brownian motion formula, Annals of Probability, 3, 234, 10.1214/aop/1176996395 Lehoczky, 1977, Formulas for stopped diffusion processes with stopping times based on the maximum, Annals of Probability, 5, 601, 10.1214/aop/1176995770 Hadjiliadis, 2006, Drawdowns preceding rallies in a Brownian motion process, Quantitative Finance, 6, 403, 10.1080/14697680600764227 Poor, 2008 Hadjiliadis, 2006, Optimal and asymptotically optimal CUSUM rules for change point detection in the Brownian motion model with multiple alternatives, Theory of Probability and its Applications, 50, 131, 10.1137/S0040585X97981494 Khan, 2008, Distributional properties of CUSUM stopping times, Sequential Analysis, 27, 420, 10.1080/07474940802446178 Magdon-Ismail, 2004, On the maximum drawdown of a Brownian motion, Journal of Applied Probability, 41, 10.1239/jap/1077134674 A. Cherny, B. Dupire, On certain distributions associated with the range of martingales, 2007, Preprint Salminen, 2007, On maximum increase and decrease of Brownian motion, Annales de l’Institut Henri Poincare (B) Probability and Statistics, 43 Vecer, 2006, Maximum drawdown and directional trading, Risk, 19, 88 Grossman, 1993, Optimal investment strategies for controlling drawdowns, Mathematical Finance, 3, 241, 10.1111/j.1467-9965.1993.tb00044.x Cvitanic, 1995, On portfolio optimization under drawdown constraints, IMA Lecture Notes in Mathematics & Applications, 65, 77 Chekhlov, 2005, Drawdown measure in portfolio optimization, International Journal of Theoretical and Applied Finance, 8, 13, 10.1142/S0219024905002767 Meilijson, 2003, The time to a given drawdown in Brownian motion, Seminaire de Probabilités, XXXVII, 94 Obloj, 2006, On local martingale and its supremum: Harmonic functions and beyond, 517 Nikeghbali, 2006, A class of remarkable submartingales, Stochastic Processes and their Applications, 116, 917, 10.1016/j.spa.2005.12.003 Kemp, 1961, The average run-length of the cumulative sum chart when a V-mask is used, Journal of the Royal Statistical Society B, 23, 149 van Dobben De Bruyn, 1968 Bissell, 1969, Cusum techniques for quality control, Applied Statistics, 18, 1, 10.2307/2346436 Woodall, 1984, On the Markov chain approach to the two-sided CUSUM procedure, Technometrics, 26, 41, 10.1080/00401706.1984.10487920 Barnard, 1959, Control charts and stochastic processes, Journal of the Royal Statistical Society: B, 21, 239