Publications (click on the first/last word in the title for a ps/pdf file):

• The Gapeev-Shiryaev conjecture. Research Report No. 2 (2023), Probab. Statist. Group Manchester (with P. A. Ernst) (24 pp). Submitted.
• An optimal stopping problem for reflecting Brownian motions. Research Report No. 1 (2023), Probab. Statist. Group Manchester (with P. V. Gapeev) (18 pp). Submitted.
• Quickest real-time detection of multiple Brownian drifts. Research Report No. 2 (2022), Probab. Statist. Group Manchester (with P. A. Ernst and H. Mei) (26 pp). To appear in SIAM J. Control Optim.
• Weak solutions in the sense of Schwartz to Dynkin's characteristic operator equation. Research Report No. 1 (2022), Probab. Statist. Group Manchester (20 pp). Submitted.
• On Newton's first law of motion. Research Report No. 1 (2021), Probab. Statist. Group Manchester (6 pp). Axioms, Vol. 11, Issue 7 (319), 2022, (1-5).
• Sticky Feller diffusions. Research Report No. 1 (2020), Probab. Statist. Group Manchester (with David Roodman) (32 pp). Electron. J. Probab. 28, 2023, (1-28).
• Sticky Bessel diffusions. Research Report No. 5 (2019), Probab. Statist. Group Manchester (24 pp). Stochastic Process. Appl. 150, 2022, (1015-1036).
• Quickest real-time detection of a Brownian coordinate drift. Research Report No. 15 (2018), Probab. Statist. Group Manchester (with P. A. Ernst) (22 pp). Ann. Appl. Probab. 32, 2022, (2652-2670).
• Optimal real-time detection of a drifting Brownian coordinate. Research Report No. 1 (2018), Probab. Statist. Group Manchester (with P. A. Ernst and Q. Zhou) (37 pp). Ann. Appl. Probab. 30, 2020, (1032-1065).
• Quickest detection problems for Ornstein-Uhlenbeck processes. Research Report No. 11 (2017), Probab. Statist. Group Manchester (with Kristoffer Glover) (29 pp). To appear in Math. Oper. Res.
• Detecting the presence of a random drift in Brownian motion. Research Report No. 10 (2017), Probab. Statist. Group Manchester (with P. Johnson, J. L. Pedersen and C. Zucca) (25 pp). Stochastic Process. Appl. 150, 2022, (1068-1090).
• Global C^1 regularity of the value function in optimal stopping problems. Research Report No. 13 (2016), Probab. Statist. Group Manchester (with T. De Angelis) (29 pp). Ann. Appl. Probab. 30, 2020, (1007-1031).
• Constrained dynamic optimality and binomial terminal wealth. Research Report No. 12 (2016), Probab. Statist. Group Manchester (with J. L. Pedersen) (17 pp). SIAM J. Control Optim. 56, 2018, (1342-1357).
• Continuity of the optimal stopping boundary for two-dimensional diffusions. Research Report No. 4 (2015), Probab. Statist. Group Manchester (23 pp). Ann. Appl. Probab. 29, 2019, (505-530).
• Quickest detection problems for Bessel processes. Research Report No. 6 (2015), Probab. Statist. Group Manchester (with Peter Johnson) (47 pp). Ann. Appl. Probab. 27, 2017, (1003-1056).
• Sequential testing problems for Bessel processes. Research Report No. 24 (2014), Probab. Statist. Group Manchester (with Peter Johnson) (29 pp). Trans. Amer. Math. Soc. 370, 2018, (2085-2113).
• On boundary behaviour of one-dimensional diffusions: From Brown to Feller and beyond. Research Report No. 8 (2014), Probab. Statist. Group Manchester (14 pp). William Feller, Selected Papers II, Springer, 2015, (77-93).
• Optimal mean-variance portfolio selection. Research Report No. 14 (2013), Probab. Statist. Group Manchester (with J. L. Pedersen) (26 pp). Math. Financ. Econ. 11, 2017, (137-160).
• Optimal prediction of resistance and support levels. Research Report No. 11 (2013), Probab. Statist. Group Manchester (with T. De Angelis) (18 pp). Appl. Math. Finance. 23, 2016, (465-483).
• Optimal mean-variance selling strategies. Research Report No. 12 (2012), Probab. Statist. Group Manchester (with J. L. Pedersen) (20 pp). Math. Financ. Econ. 10, 2016, (203-220).
• Stochastic differential equations for sticky Brownian motion. Research Report No. 5 (2012), Probab. Statist. Group Manchester (with H. J. Engelbert) (28 pp). Stochastics 86, 2014, (993-1021).
• A probabilistic solution to the Stroock-Williams equation. Research Report No. 18 (2011), Probab. Statist. Group Manchester (9 pp). Ann. Probab. 42, 2014, (2197-2206).
• Embedding laws in diffusions by functions of time. Research Report No. 10 (2011), Probab. Statist. Group Manchester (with A. M. G. Cox) (27 pp). Ann. Probab. 43, 2015, (2481-2510).
• Three-dimensional Brownian motion and the golden ratio rule. Research Report No. 5 (2011), Probab. Statist. Group Manchester (with K. Glover and H. Hulley) (26 pp). Ann. Appl. Probab. 23, 2013, (895-922).
• Quickest detection of a hidden target and extremal surfaces. Research Report No. 23 (2010), Probab. Statist. Group Manchester (28 pp). Ann. Appl. Probab. 24, 2014, (2340-2370).
• Optimal detection of a hidden target: The median rule. Research Report No. 8 (2010), Probab. Statist. Group Manchester (15 pp). Stochastic Process. Appl. 122, 2012, (2249-2263).
• A duality principle for the Legendre transform. Research Report No. 2 (2010), Probab. Statist. Group Manchester (22 pp). J. Convex Anal. 19, 2012, (609-630).
• Predicting the ultimate supremum of a stable Levy process with no negative jumps. Research Report No. 28 (2009), Probab. Statist. Group Manchester (with V. Bernyk and R. C. Dalang) (33 pp). Ann. Probab. 39, 2011, (2385-2423).
• The British Russian option. Research Report No. 11 (2009), Probab. Statist. Group Manchester (with K. Glover and F. Samee) (19 pp). Stochastics 80, 2011, (315-332).
• The British Asian option. Research Report No. 5 (2009), Probab. Statist. Group Manchester (with K. Glover and F. Samee) (17 pp). Sequential Anal. 29, 2010, (311-327).
• Selling a stock at the ultimate maximum. Research Report No. 10 (2008), Probab. Statist. Group Manchester (with J. du Toit) (28 pp). Ann. Appl. Probab. 19, 2009, (983-1014).
• The British call option. Research Report No. 2 (2008), Probab. Statist. Group Manchester (with F. Samee) (25 pp). Quant. Finance 13, 2013, (95-109).
• The British put option. Research Report No. 1 (2008), Probab. Statist. Group Manchester (with F. Samee) (25 pp). Appl. Math. Finance 18, 2011 (537-563).
• The law of the hitting times to points by a stable Levy process with no negative jumps. Research Report No. 15 (2007), Probab. Statist. Group Manchester (8 pp). Electron. Commun. Probab. 13, 2008, (653-659).
• Predicting the last zero of Brownian motion with drift. Research Report No. 10 (2007), Probab. Statist. Group Manchester (with J. du Toit and A. N. Shiryaev) (17 pp). Stochastics 80, 2008, (229-245).
• Predicting the time of the ultimate maximum for Brownian motion with drift. Research Report No. 4 (2007), Probab. Statist. Group Manchester (with J. du Toit) (16 pp). Proc. Math. Control Theory Finance (Lisbon 2007), Springer, 2008, (95-112).
• The law of the supremum of a stable Levy process with no negative jumps. Research Report No. 29 (2006), Probab. Statist. Group Manchester (with V. Bernyk and R. C. Dalang) (13 pp). Ann. Probab. 36, 2008, (1777-1789).
• Optimal stopping games and Nash equilibrium. Research Report No. 28 (2006), Probab. Statist. Group Manchester (15 pp). Theory Probab. Appl. 53, 2008, (558-571).
• Optimal stopping games for Markov processes. Research Report No. 15 (2006), Probab. Statist. Group Manchester (with E. Ekstrom) (21 pp). SIAM J. Control Optim. 47, 2008, (684-702).
• Principle of smooth fit and diffusions with angles. Research Report No. 7 (2006), Probab. Statist. Group Manchester (11 pp). Stochastics 79, 2007, (293-302).
• Optimal stopping and free-boundary problems. (Co-author: A. N. Shiryaev). Lectures in Mathematics, ETH Zurich, Birkhauser, 2006, (500 pp). To order a copy click here. [Read AMS review. Read Zentralblatt review.]
• On reflecting Brownian motion with drift. Research Report No. 3 (2005), Probab. Statist. Group Manchester (8 pp). Proc. Symp. Stoch. Syst. (Osaka 2005), ISCIE Kyoto, 2006, (1-5).
• The trap of complacency in predicting the maximum. Research Report No. 2 (2005), Probab. Statist. Group Manchester (with J. du Toit) (23 pp). Ann. Probab. 35, 2007, (340-365).
• On the fundamental solution of the Kolmogorov-Shiryaev equation. Research Report No. 438 (2004), Dept. Theoret. Statist. Aarhus (11 pp). Research Report No. 1 (2005), Probab. Statist. Group Manchester (11 pp). The Shiryaev Festschrift (Metabief, 2005), Springer, 2006, (535-546).
• A change-of-variable formula with local time on surfaces. Research Report No. 437 (2004), Dept. Theoret. Statist. Aarhus (23 pp). Sem. de Probab. XL, Lecture Notes in Math. 1899, Springer, 2007, (69-96).
• On Asian options of American type. Research Report No. 436 (2003), Dept. Theoret. Statist. Aarhus (with N. Uys) (19 pp). Exotic Option Pricing and Advanced Levy Models (Eindhoven, 2004), John Wiley, 2005, (217-235).
• The Wiener disorder problem with finite horizon. Research Report No. 435 (2003), Dept. Theoret. Statist. Aarhus (with P. V. Gapeev) (23 pp). Stochastic Process. Appl. 116, 2006, (1770-1791).
• The Wiener sequential testing problem with finite horizon. Research Report No. 434 (2003), Dept. Theoret. Statist. Aarhus (with P. V. Gapeev) (18 pp). Stoch. Stoch. Rep. 76, 2004, (59-75).
• The Russian option: Finite horizon. Research Report No. 433 (2003), Dept. Theoret. Statist. Aarhus (16 pp). Finance Stoch. 9, 2005 (251-267).
• On the American option problem. Research Report No. 431 (2002), Dept. Theoret. Statist. Aarhus (13 pp). Math. Finance 15, 2005, (169-181).
• Local time-space calculus and extensions of Ito's formula. Research Report No. 430 (2002), Dept. Theoret. Statist. Aarhus (with R. Ghomrasni) (15 pp). Proc. High Dim. Probab. III (Sandbjerg 2002), Progr. Probab. 55, Birkhauser Basel, 2003, (177-192).
• A change-of-variable formula with local time on curves. Research Report No. 428 (2002), Dept. Theoret. Statist. Aarhus (30 pp). J. Theoret. Probab. 18, 2005, (499-535).
• On nonlinear integral equations arising in problems of optimal stopping. Research Report No. 426 (2002), Dept. Theoret. Statist. Aarhus (with J. L. Pedersen) (17 pp). Proc. Funct. Anal. VII (Dubrovnik 2001), Various Publ. Ser. Aarhus 46, 2002, (159-175).
• Maximum process problems in optimal control theory. Research Report No. 423 (2001), Dept. Theoret. Statist. Aarhus (12 pp). J. Appl. Math. Stochastic Anal. 2005, 2005, (77-88).
• On integral equations arising in the first-passage problem for Brownian motion. Research Report No. 421 (2001), Dept. Theoret. Statist. Aarhus (20 pp). J. Integral Equations Appl. 14, 2002, (397-423).
• Limit at zero of the Brownian first-passage density. Research Report No. 420 (2001), Dept. Theoret. Statist. Aarhus (12 pp). Probab. Theory Related Fields. 124, 2002, (100-111).
• Principles of optimal stopping and free-boundary problems. D.Sc. thesis, Faculty of Mathematics, University of Aarhus. Lecture Notes Series. No. 68 (2001), Dept. Math. Univ. Aarhus (95 pp).
• Solving the Poisson disorder problem. Research Report No. 419 (2000), Dept. Theoret. Statist. Aarhus (with A. N. Shiryaev) (17 pp). Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann, Springer, 2002, (295-312).
• On the diffusion coefficient: The Einstein relation and beyond. Research Report No. 416 (2000) & No. 424 (2001), Dept. Theoret. Statist. Aarhus (21 pp). Stoch. Models 19, 2003, (383-405).
• A note on the call-put parity and a call-put duality. Research Report No. 413 (2000), Dept. Theoret. Statist. Aarhus (with A. N. Shiryaev) (5 pp). Theory Probab. Appl. 46, 2001, (181-183).
• From uniform laws of large numbers to uniform ergodic theorems. Lecture Notes Series. No. 66 (2000), Dept. Math. Univ. Aarhus (142 pp).
• Bounding the maximal height of a diffusion by the time elapsed. Research Report No. 412 (1999), Dept. Theoret. Statist. Aarhus (9 pp). J. Theoret. Probab. 14, 2001, (845-855).
• Levy-Khintchine inequalities, multiple reflection, and Brownian motion. Research Report No. 411 (1999), Dept. Theoret. Statist. Aarhus (18 pp). Proc. Funct. Anal. VI (Dubrovnik 1999), Various Publ. Ser. Aarhus 45, 2000, (27-44).
• Maximal inequalities for reflected Brownian motion with drift. Research Report No. 409 (1999), Dept. Theoret. Statist. Aarhus (with A. N. Shiryaev) (8 pp). Theory Probab. Math. Statist. 63, 2001, (137-143).
• The Azema-Yor embedding in non-singular diffusions. Research Report No. 406 (1999), Dept. Theoret. Statist. Aarhus (with J. L. Pedersen) (14 pp). Stochastic Process. Appl. 96, 2001, (305-312).
• Stopping Brownian motion without anticipation as close as possible to its ultimate maximum. Research Report No. 405 (1999), Dept. Theoret. Statist. Aarhus (with S. E. Graversen and A. N. Shiryaev) (11 pp). Theory Probab. Appl. 45, 2000, (125-136).
• Market forces and dynamic asset pricing. Research Report No. 402 (1998), Dept. Theoret. Statist. Aarhus (with J. Shorish) (49 pp). Stochastic Anal. Appl. 20, 2002, (1027-1082).
• Sequential testing problems for Poisson processes. Research Report No. 400 (1998), Dept. Theoret. Statist. Aarhus (with A. N. Shiryaev) (20 pp). Ann. Statist. 28, 2000, (837-859).
• The Azema-Yor embedding in Brownian motion with drift. Research Report No. 398 (1998), Dept. Theoret. Statist. Aarhus (12 pp). Proc. High Dim. Probab. II (Seattle 1999), Progr. Probab. 47, Birkhauser Boston, 2000, (207-221).
• Maximal inequalities for the Ornstein-Uhlenbeck process. Research Report No. 393 (1998), Dept. Theoret. Statist. Aarhus (with S. E. Graversen) (8 pp). Proc. Amer. Math. Soc. 128, 2000, (3035-3041).
• Controlling the velocity of Brownian motion by its terminal value. Research Report No. 391 (1998), Dept. Theoret. Statist. Aarhus (11 pp). Anal. Geom. Inequal. Appl. (invited paper), Math. Appl. 478, 1999, (323-333).
• Solving non-linear optimal stopping problems by the method of time-change. Research Report No. 390 (1997), Dept. Theoret. Statist. Aarhus (with J. L. Pedersen) (24 pp). Stochastic Anal. Appl. 18, 2000, (811-835).
• Designing options given the risk: The optimal Skorokhod-embedding problem. Research Report No. 389 (1997), Dept. Theoret. Statist. Aarhus (18 pp). Stochastic Process. Appl. 81, 1999, (25-38).
• A true buyer's risk and classification of options. Research Report No. 386 (1997), Dept. Theoret. Statist. Aarhus (20 pp). Inform. Technol. Econom. Management 1 (inaugural issue), 2001, (1-20).
• Optimal stopping of the maximum process: The maximality principle. Research Report No. 377 (1997), Dept. Theoret. Statist. Aarhus (30 pp). Ann. Probab. 26, 1998, (1614-1640).
• On the Brownian first-passage time over a one-sided stochastic boundary. Research Report No. 371 (1997), Dept. Theoret. Statist. Aarhus (with A. N. Shiryaev) (11 pp). Theory Probab. Appl. 42, 1997, (591-602).
• Computing the expectation of the Azema-Yor stopping time. Research Report No. 364 (1996), Dept. Theoret. Statist. Aarhus (with J. L. Pedersen) (10 pp). Ann. Inst. H. Poincare Probab. Statist. 34, 1998, (265-276).
• The best Doob-type bounds for the maximum of Brownian paths. Research Report No. 363 (1996), Dept. Theoret. Statist. Aarhus (9 pp). Proc. High Dim. Probab. I (Oberwolfach 1996), Progr. Probab. 43, Birkhauser Basel, 1998, (287-296).
• Optimal stopping in the L log L-inequality of Hardy and Littlewood. Research Report No. 360 (1996), Dept. Theoret. Statist. Aarhus (with S. E. Graversen) (12 pp). Bull. London Math. Soc. 30, 1998, (171-181).
• The integral analogue of the Hardy-Littlewood L log L-inequality for Brownian motion. Research Report No. 359 (1996), Dept. Theoret. Statist. Aarhus (12 pp). Math. Inequal. Appl. 1, 1998, (137-148).
• Optimal stopping inequalities for the integral of Brownian paths. Research Report No. 355 (1996), Dept. Theoret. Statist. Aarhus (9 pp). J. Math. Anal. Appl. 222, 1998, (244-254).
• On Doob's maximal inequality for Brownian motion. Research Report No. 337 (1995), Dept. Theoret. Statist. Aarhus (with S. E. Graversen), (13 pp). Stochastic Process. Appl. 69, 1997, (111-125).
• Optimal stopping and maximal inequalities for linear diffusions. Research Report No. 335 (1995), Dept. Theoret. Statist. Aarhus (with S. E. Graversen) (18 pp). J. Theoret. Probab. 11, 1998, (259-277).
• Optimal stopping and maximal inequalities for geometric Brownian motion. Research Report No. 330 (1995), Dept. Theoret. Statist. Aarhus (with S. E. Graversen) (18 pp). J. Appl. Probab. 35, 1998, (856-872).
• On the Russian option: The expected waiting time. Research Report No. 325 (1995), Dept. Theoret. Statist. Aarhus (with S. E. Graversen) (11 pp). Theory Probab. Appl. 42, 1997, (564-575).
• Extremal problems in the maximal inequalities of Khintchine. Preprint Ser. No. 8 (1995), Math. Inst. Aarhus (with S. E. Graversen) (14 pp). Math. Proc. Cambridge Philos. Soc. 123, 1998, (169-177).
• Khinchine inequalities and a martingale extension of the sphere of their action. Preprint Ser. No. 24 (1994), Math. Inst. Aarhus (with A. N. Shiryaev) (55 pp). Uspekhi Mat. Nauk. 50, 1995, (3-62), (Russian). Russian Math. Surveys 50, 1995, (849-904), (English).
• Maximal inequalities for Bessel processes. Preprint Ser. No. 23 (1994), Math. Inst. Aarhus (with S. E. Graversen) (15 pp). J. Inequal. Appl. 2, 1998, (99-119).
• On the exponential Orlicz norms of stopped Brownian motion. Preprint Ser. No. 17 (1994), Math. Inst. Aarhus (20 pp). Studia Math. 117, 1996, (253-273).
• On Wald-type optimal stopping for Brownian motion. Preprint Ser. No. 10 (1994), Math. Inst. Aarhus (with S. E. Graversen), (15 pp). J. Appl. Probab. 34, 1997, (66-73).
• Randomly weighted series of contractions in Hilbert spaces. Preprint Ser. No. 5 (1994), Math. Inst. Aarhus (with D. Schneider and M. Weber) (15 pp). Math. Scand. 79, 1996, (263-282).
• The uniform mean-square ergodic theorem for wide sense stationary processes. Preprint Ser. No. 29 (1993), Math. Inst. Aarhus (19 pp). Stochastic Anal. Appl. 16, 1998, (697-720).
• Best constants in Kahane-Khintchine inequalities for complex Steinhaus variables. Preprint Ser. No. 24 (1993), Math. Inst. Aarhus (10 pp). Proc. Amer. Math. Soc. 123, 1995, (3101-3111).
• Uniform ergodic theorems for dynamical systems under VC entropy conditions. Preprint Ser. No. 15 (1993), Math. Inst. Aarhus (with Joseph E. Yukich) (25 pp). Proc. Probab. Banach Spaces IX (Sandbjerg 1993), Progr. Probab. 35, Birkhauser Boston, 1994, (104-127).
• The uniform ergodic theorem for dynamical systems. Preprint Ser. No. 14 (1993), Math. Inst. Aarhus (with M. Weber) (30 pp). Proc. Convergence in Ergodic Theory and Probability (Columbus 1993), Ohio State Univ. Math. Res. Inst. Publ. 5, 1996, (305-332).
• On the central limit theorem for aperiodic dynamical systems and applications. Preprint Ser. No. 11 (1993), Math. Inst. Aarhus, (with M. Weber, S. Ladouceur and T. de la Rue) (21 pp). Theory Probab. Math. Statist. 57, 1997, (140-159).
• Consistency of statistical models in the stationary case. Preprint Ser. No. 39 (1992), Math. Inst. Aarhus (21 pp). Math. Scand. 78, 1996, (293-319).
• Measure compact sets of functions and consistency of statistical models. Preprint Ser. No. 38 (1992), Math. Inst. Aarhus (10 pp). Theory Probab. Appl. 38, 1993, (360-367).
• Maximal inequalities of Kahane-Khintchine's type in Orlicz spaces. Preprint Ser. No. 33 (1992), Math. Inst. Aarhus (18 pp). Math. Proc. Cambridge Philos. Soc. 115, 1994, (175-190).
• The continuity principle in exponential type Orlicz spaces. Preprint Ser. No. 32 (1992), Math. Inst. Aarhus (with S. E. Graversen and M. Weber) (19 pp). Nagoya Math. J. 137, 1995, (55-75).
• Necessary and sufficient conditions for the uniform law of large numbers in the stationary case. Preprint Ser. No. 27 (1992), Math. Inst. Aarhus (with M. Weber) (26 pp). Proc. Funct. Anal. IV (Dubrovnik 1993), Various Publ. Ser. Aarhus 43, 1994, (165-190).
• Uniform convergence of reversed martingales. Preprint Ser. No. 21 (1992), Math. Inst. Aarhus (27 pp). J. Theoret. Probab. 8, 1995, (387-415).
• Best constants in Kahane-Khintchine inequalities in Orlicz spaces. Preprint Ser. No. 10 (1992), Math. Inst. Aarhus (42 pp). J. Multivariate Anal. 45, 1993, (183-216).
• Consistency of statistical models described by families of reversed submartingales. Preprint Ser. No. 9 (1992), Math. Inst. Aarhus, (26 pp). Probab. Math. Statist. 18, 1998, (289-318).
• The existence of measurable approximating maximums. Preprint Ser. No. 29 (1991), Math. Inst. Aarhus (13 pp). Math. Scand. 77, 1995, (71-84).
• Vitali convergence theorem for upper integrals. Preprint Ser. No. 28 (1991), Math. Inst. Aarhus (14 pp). Proc. Funct. Anal. IV (Dubrovnik 1993), Various Publ. Ser. Aarhus 43, 1994, (191-203).
• On separability of families of reversed submartingales. Preprint Ser. No. 27 (1991), Math. Inst. Aarhus (26 pp). Proc. Probab. Banach Spaces IX (Sandbjerg 1993), Progr. Probab. 35, Birkhauser Boston, 1994, (36-53).
• Perfect measures and maps. Preprint Ser. No. 26 (1991), Math. Inst. Aarhus (34 pp).
• Extending finite measures to perturbed sigma-algebras. Preprint Ser. No. 25 (1991), Math. Inst. Aarhus (25 pp). Proc. Funct. Anal. V (Dubrovnik 1997), Various Publ. Ser. Aarhus 44, 1998, (77-104).
• A necessary and sufficient condition for the extension of a finite measure. Glas. Mat. Ser. III, Vol. 27 (47), No. 1, 1992, (31-48).