Quickest Detection Problems for Ornstein–Uhlenbeck Processes

References

• [1] Assing S, Jacka S, Ocejo A (2014) Monotonicity of the value function for a two-dimensional optimal stopping problem. Ann. Appl. Probab. 24(4):1554–1584.Crossref, Google Scholar
• [2] Avellaneda M, Lee J (2010) Statistical arbitrage in the US equities market. Quant. Finance 10(7):761–782.Crossref, Google Scholar
• [3] Bertram W (2010) Analytic solutions for optimal statistical arbitrage trading. Physica A: Statist. Mechanics Its Appl. 389(11):2234–2243.Crossref, Google Scholar
• [4] Blumenthal RM, Getoor RK (1968) Markov Processes and Potential Theory (Academic Press, Cambridge, MA).Google Scholar
• [5] Chen H, Chen S, Chen Z, Li F (2019) Empirical investigation of an equity pairs trading strategy. Management Sci. 65(1):370–389.Link, Google Scholar
• [6] De Angelis T, Peskir G (2020) Global C1 regularity of the value function in optimal stopping problems. Ann. Appl. Probab. 30(3):1007–1031.Crossref, Google Scholar
• [7] Do B, Faff R (2010) Does simple pairs trading still work? Financial Analysts J. 66(4):83–95.Crossref, Google Scholar
• [8] Du Toit J, Peskir G (2009) Selling a stock at the ultimate maximum. Ann. Appl. Probab. 19(3):983–1014.Crossref, Google Scholar
• [9] Ehrman DS (2006) The Handbook of Pairs Trading: Strategies Using Equities, Options, and Futures (John Wiley, Hoboken, NJ).Google Scholar
• [10] Ekström E, Lindberg C, Tysk J (2011) Optimal liquidation of a pairs trade. Di Nunno G, Øksendal B, eds. Advanced Mathematical Methods for Finance (Springer, Berlin), 247–255.Crossref, Google Scholar
• [11] Elliott R, Van Der Hoek J, Malcolm W (2005) Pairs trading. Quant. Finance 5(3):271–276.Crossref, Google Scholar
• [12] Engelbert HJ, Peskir G (2014) Stochastic differential equations for sticky Brownian motion. Stochastics 86(6):993–1021.Crossref, Google Scholar
• [13] Feller W (1951) Two singular diffusion problems. Ann. Math. 54(1):173–182.Crossref, Google Scholar
• [14] Feller W (1952) The parabolic differential equations and the associated semi-groups of transformations. Ann. Math. 55(3):468–519.Crossref, Google Scholar
• [15] Ferreyra G, Sundar P (2000) Comparison of solutions of stochastic equations and applications. Stochastic Anal. Appl. 18:211–229.Crossref, Google Scholar
• [16] Gapeev PV, Peskir G (2006) The Wiener disorder problem with finite horizon. Stochastic Processes Their Appl. 116(12):1770–1791.Crossref, Google Scholar
• [17] Gapeev PV, Shiryaev AN (2013) Bayesian quickest detection problems for some diffusion processes. Adv. Appl. Probab. 45(1):164–185.Crossref, Google Scholar
• [18] Gatev E, Goetzmann WN, Rouwenhorst KG (2006) Pairs trading: Performance of a relative-value arbitrage rule. Rev. Financial Stud. 19(3):797–827.Crossref, Google Scholar
• [19] Jacobs H, Weber M (2015) On the determinants of pairs trading profitability. J. Financial Markets 23:75–97.Crossref, Google Scholar
• [20] Johnson P, Peskir G (2017) Quickest detection problems for Bessel processes. Ann. Appl. Probab. 27(2):1003–1056.Crossref, Google Scholar
• [21] Kitapbayev Y, Leung T (2017) Optimal mean-reverting spread trading: Nonlinear integral equation approach. Ann. Finance 13:181–203.Crossref, Google Scholar
• [22] Krauss C (2017) Statistical arbitrage pairs trading strategies: Review and outlook. J. Econom. Surveys 31(2):513–545.Crossref, Google Scholar
• [23] Leung T, Li X (2015) Optimal mean reversion trading with transaction costs & stop-loss exit. Internat. J. Theoretical Appl. Finance 18(3):1550020.Crossref, Google Scholar
• [24] Leung T, Li X (2016) Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications (World Scientific, Singapore).Crossref, Google Scholar
• [25] Lindberg C (2014) Pairs trading with opportunity cost. J. Appl. Probab. 51(1):282–286.Crossref, Google Scholar
• [26] Lowenstein R (2000) When Genius Failed: The Rise and Fall of Long-Term Capital Management (Random House, New York).Google Scholar
• [27] Peskir G (2005) On the American option problem. Math. Finance 15(1):169–181.Crossref, Google Scholar
• [28] Peskir G (2007) A change-of-variable formula with local time on surfaces. Donati-Martin C, Émery M, Rouault A, Stricker C, eds. Séminaire de Probabilités XL. Lecture Notes in Mathematics, vol. 1899 (Springer, Berlin), 69–96.Crossref, Google Scholar
• [29] Peskir G (2015) On boundary behaviour of one-dimensional diffusions: From Brown to Feller and beyond. Schilling RL, Vondraček Z, Woyczyński WA, eds. William Feller, Selected Papers II (Springer, Cham, Switzerland), 77–93.Crossref, Google Scholar
• [30] Peskir G (2019) Continuity of the optimal stopping boundary for two-dimensional diffusions. Ann. Appl. Probab. 29(1):505–530.Crossref, Google Scholar
• [31] Peskir G (2022) Weak solutions in the sense of Schwartz to Dynkin’s characteristic operator equation. Research Report No. 1, Probability and Statistics Group, University of Manchester, Manchester, UK.Google Scholar
• [32] Peskir G, Shiryaev AN (2006) Optimal Stopping and Free-Boundary Problems. Lectures in Mathematics, ETH Zürich (Birkhäuser, Basel).Google Scholar
• [33] Phillips PCB, Yu J (2011) Dating the timeline of financial bubbles during the subprime crisis. Quant. Econom. 2(3):455–491.Crossref, Google Scholar
• [34] Phillips PCB, Wu Y, Yu J (2011) Explosive behavior in the 1990s NASDAQ: When did exuberance escalate asset values? Internat. Econom. Rev. 52(1):201–226.Crossref, Google Scholar
• [35] Rogers LCG, Williams D (2000) Diffusions, Markov Processes and Martingales: Itô Calculus, vol. 2 (Cambridge University Press, Cambridge, UK).Google Scholar
• [36] Shiryaev AN (1961) The problem of the most rapid detection of a disturbance of a stationary regime. Soviet Math. Doklady 2:795–799.Google Scholar
• [37] Shiryaev AN (1978) Optimal Stopping Rules (Springer, Berlin).Google Scholar
• [38] Shiryaev AN (1996) Probability (Springer, New York).Crossref, Google Scholar
• [39] Shiryaev AN (2002) Quickest detection problems in the technical analysis of the financial data. Geman H, Madan D, Pliska SR, Vorst T, eds. Mathematical Finance—Bachelier Congress 2000 (Springer, Berlin), 487–521.Crossref, Google Scholar
• [40] Shiryaev AN (2010) Quickest detection problems: Fifty years later. Sequential Anal. 29(4):345–385.Crossref, Google Scholar
• [41] Song Q, Zhang Q (2013) An optimal pairs-trading rule. Automatica 49(10):3007–3014.Crossref, Google Scholar
• [42] Song Q, Yin G, Zhang Q (2009) Stochastic optimization methods for buying-low-and-selling-high strategies. Stochastic Anal. Appl. 27(3):523–542.Crossref, Google Scholar
• [43] Uhlenbeck GE, Ornstein LS (1930) On the theory of Brownian motion. Physical Rev. 36(5):823–841.Crossref, Google Scholar
• [44] Vidyamurphy G (2004) Pairs Trading: Quantitative Methods and Analysis (John Wiley, Hoboken, NJ).Google Scholar
• [45] Whistler M (2004) Trading Pairs: Capturing Profits and Hedging Risk with Statistical Arbitrage Strategies (John Wiley, Hoboken, NJ).Google Scholar