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Department of Statistics

David Hobson's Publications Page

Papers in press and preprints are listed below.

Published Work

  1. Limit theorems for transient diffusions on the line. Co-author: L.C.G. Rogers. Probability Theory and Related Fields, 89, pp61-74, 1991.
  2. Recurrence and transience of reflecting Brownian motion in the plane. Co-author: L.C.G. Rogers. Mathematical Proceedings of the Cambridge Philosophical Society, 113, pp387-400, 1993.
  3. Asymptotics for an Arcsin type result. Annales de l`Institute Henri Poincare, Probabilites et Statistiques, 30, pp235-243, 1994.
  4. Escape rates for transient reflected Brownian motions in wedges and cones. Co-authors: R.D. DeBlassie, E.A. Housworth and E.H. Toby. Stochastics and Stochastic Reports, 57, pp199-211, 1996.
  5. Non-colliding Brownian motions on the circle. Co-author: W. Werner. Bulletin of the London Mathematical Society, 135, pp643-650, 1996.
  6. Complete models with stochastic volatility. Co-author: L.C.G. Rogers, Mathematical Finance. 8, pp27--48, 1998.
  7. Stochastic Volatility, In Statistics in Finance, editors D. Hand and S. Jacka, Applications of Statistics Series, Arnold, London. 1998.
  8. Volatility mis-specification, option pricing and super-replication via coupling. Annals of Applied Probability, 8, pp193-205, 1998.
  9. Robust hedging of the lookback option, Finance and Stochastics, 2, pp329-347, 1998.
  10. The maximum maximum of a martingale, Seminaire de Probabilites. XXXII, pp250-263, 1998.
  11. Taylor expansions of curve-crossing probabilities, Co-authors: D. Williams and A.T.A Wood, Bernouilli 5, pp779-795, 1999.
  12. Local time, coupling and the passport option, Co-author: V. Henderson. Finance and Stochastics, 4, pp69-80, 2000.
  13. Marked excursions and random trees. Seminaire de Probabilites. XXXIV, pp289-301, 2000.
  14. CEO age and top executive pay: a UK empirical study, Co-authors: P.J. McKnight, C. Tomkins and C. Weir. Journal of Management and Governance. 4, pp173-187, 2000.
  15. Robust hedging of barrier options, Co-authors: H.M. Brown and L.C.G. Rogers. Mathematical Finance. 11, pp285-314, 2001.
  16. The maximum maximum of a martingale constrained by an intermediate law, Co-authors: H.M. Brown and L.C.G. Rogers. Probability Theory and Related Fields. 119, pp558-578, 2001.
  17. Some consequences of the cyclic exchangeabiltity property for exponential functionals of Levy processes, Co-authors, L. Chaumont and M. Yor. Seminaire de Probabilites. XXXV, pp334-347, 2001. Electronic version for those with appropriate permissions.
  18. Passport options with stochastic volatility, Co-author: V. Henderson. Applied Mathematical Finance 8, pp97-118, 2001.
  19. Substitute hedging, Co-author: V. Henderson. Risk Magazine 15/5, pp71-75, 2002. Reprinted in Exotic Options: The Cutting-edge Collection, Editor: A. Lipton, Risk Books 2003.
  20. A new class of commodity hedging strategies: a passport options approach, Co-authors: V. Henderson and G. Kentwell. International Journal of Theoretical and Applied Finance 5, pp255-278, 2002. FORC preprint 2001/113 .
  21. The minimum maximum of a continuous martingale with given initial and terminal laws, Co-author: J.L. Pedersen. Annals of Probability . 30, pp978-999, 2002.
  22. Real Options with Constant Relative Risk Aversion, Co-author: V. Henderson. Journal of Economic Dynamics and Control. 27, pp329-355, 2002.
  23. Coupling and Option Price Comparisons in a Jump-Diffusion Model, Co-author: V. Henderson. Stochastics and Stochastics Reports. 75, pp79-101, 2003.
  24. An optimal Skorokhod embedding for diffusions, Co-author: A.M.G. Cox. Stochastic Processes and Applications. 111, 17-39, 2004.
  25. Stochastic Volatility Models, Correlation and the q-optimal Measure. Mathematical Finance. 14, 537-556, 2004.
  26. A Survey of Mathematical Finance, (Adams Prize Essay). Proceedings of the Royal Society: Mathematical, Physical and Engineering Sciences. 460:2052, 3369-3401, 2004. Published electronically at FirstCite October 2004.
  27. Bounds for the utility-indifference prices of non-traded assets in incomplete markets Decisions in Economics and Finance. 28, 33-52, 2005. The published version is also available for those with appropriate Springer permissions.
  28. A comparison of $q$-optimal option prices in a stochastic volatility model with correlation. Co-authors: V. Henderson, S. Howison, T.Kluge. Review of Derivatives Research 8, 5-25, June 2005.
  29. Maximising the Probability of a Perfect Hedge using an Imperfectly Correlated Instrument, Co-author: J.W.V. Penn. International Journal of Theoretical and Applied Finance, 8, 763-790, 2005. The published version is also available online.
  30. Local martingales, bubbles and option prices. Co-author: A.M.G. Cox. Finance and Stochastics, 9, 477-492, 2005. The published version is also available for those with appropriate Springer permissions.
  31. Static-arbitrage upper bounds for the prices of basket options. Co-authors: P. Laurence, T-H. Wang. Quantitative Finance 5 (#4) 329-342, August 2005.
  32. Static-arbitrage optimal subreplicating strategies for basket options. Co-authors: P. Laurence, T-H. Wang. Insurance: Mathematics and Economics, 37 (#3) 553-572, 2005.
  33. Skorokhod embeddings, minimality and non-centered target distributions. Co-author: A.M.G. Cox. Probability Theory and Related Fields, 135, 395-414, July 2006. The published version is also available for those with appropriate Springer permissions.
  34. A note on irreversible investment, hedging and optimal consumption problems. Co-authors: V. Henderson. International Journal of Theoretical and Applied Finance, 9 (#6), 997-1007, 2006. An online version is available.
  35. The range of traded options prices. Co-author: M.H.A. Davis. Mathematical Finance 17 (#1) 1-14, 2007.
  36. A short proof of an identity for a Brownian Bridge due to Donati-Martin, Matsumoto and Yor. Statistics and Probability Letters 77 (#2) 148-150 2007. Published online. DOI information: 10.1016/j.spl.2006.06.003
  37. Bounds for in-progress floating-strike Asian options using symmetry, Co-authors: V. Henderson, W. Shaw and R. Wojakowski. Annals of Operations Research. 151 (#1) 81-98, 2007. Published online. DOI 10.1007/s10479-006-0122-8 pdf version.
  38. Is there an informationally passive benchmark for option pricing incorporating maturity? Co-authors: V. Henderson, T. Kluge. Quantitative Finance 7 (#1) 75-86 2007.
  39. Optimal stopping of the maximum process: a converse to the results of Peskir Stochastics 79, 85-102, 2007. (c) Taylor & Francis, 2007. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. doi:10.1080/17442500601111429. Published online.
  40. A unifying class of Skorokhod embeddings: connecting the Az\'{e}ma-Yor and Vallois embeddings. Co-author: A.M.G. Cox. Bernoulli 13 (#1) 114-130, 2007.
  41. Horizon Unbiased Utility Functions. Co-author: V. Henderson. Stochastic Processes and Applications 117, (#11) 1621-1641, 2007. A publisher's online is available for those with appropriate permissions.
  42. Perpetual American Options in Incomplete Markets: The Infinitely Divisible Case. Co-author: V. Henderson. Quantitative Finance 8 (#5), 461-469, 2008.
  43. Optimal Timing for an Asset Sale in an Incomplete Market. Co-authors: J.D. Evans, V. Henderson. Mathematical Finance 18 (#4), 545-568, 2008.
  44. An explicit solution for an optimal stopping/optimal control problem which models an asset sale. Co-author: V. Henderson. Annals of Applied Probability 18 #5, 1681-1705, 2008. DOI: 10.1214/07-AAP511.
  45. Pathwise inequalities of the local time: applications to Skorokhod embeddings and optimal stopping. Co-authors: A. Cox and J.Obloj. Annals of Applied Probability 18 #5, 1870-1896, 2008. DOI: 10.1214/07-AAP507.
  46. Utility Indifference Pricing: An Overview. Co-author: V. Henderson. Indifference Pricing: Theory and Applications Editor: R. Carmona, Princeton University Press. February 2009.
  47. Comparison results for stochastic volatility models via coupling. Finance and Stochastics 14 #1, 129-152, 2010. DOI: 10.1007/s00780-008-0083-7
  48. The Skorokhod Embedding Problem and Model-Independent Bounds for Option Prices.Paris-Princeton Lectures on Mathematical Finance, 2010. Springer, LNM 2003.
  49. Recovering a time-homogeneous stock price process from perpetual option prices. Co-author: E.Ekstrom. arXiv:0903.4833 Annals of Applied Probability 21 #3, 1102-1135, 2011.
  50. Time homogeneous diffusions with a given marginal at a random time. Co-authors: A.Cox, J.Obloj. arXiv:0912.1719 ESAIM: Probability and Statistics. Special issue in honour of Marc Yor. 15, S11-S24, 2011. DOI: 10.1051/ps/2010021
  51. Optimal liquidation of derivative portfolios. Co-author: V. Henderson. Mathematical Finance 21(3) 365-382, 2011. DOI: 10.1111/j.1467-9965.2010.00455.x
  52. Constructing time-homogeneous generalised diffusions consistent with optimal stopping values.Co-author: M.Klimmek arXiv:1005.0160 Stochastics 83, (4-6), 477-503, 2011. DOI:10.1080/17442508.2010.522237
  53. Robust bounds for forward start options. Co-author: A. Neuberger. Mathematical Finance 22, 31-56, 2012. DOI: 10.1111/j.1467-9965.2010.00473.x
  54. Model independent hedging strategies for variance swaps. Co-author: M. Klimmek. Finance and Stochastics 16, 611-649, 2012 (DOI) 10.1007/s00780-012-0190-3 Online published version
  55. Can time-homogeneous diffusions produce any distribution? Co-authors: E. Ekstrom, S. Janson and J. Tysk. arXiv:1103.4371 Probability Theory and Related Fields. 155, 493-520, 2013. DOI:10.1007/s00440-011-0405-0 Springer Online version.
  56. Risk aversion, indivisible timing options, and gambling. Co-author: V. Henderson. Operations Research 61, Issue 1, 126-137, Jan-Feb 2013.
  57. Maximising functionals of the joint law of the maximum and terminal value in the Skorokhod embedding problem. Co-author: M. Klimmek. arXiv:1012.3909 Annals of Applied Probability Vol. 23, No. 5, p2020-2052 2013. Access via Project Euclid
  58. Fake exponential Brownian motion. arXiv:1210.1391 Statistics and Probability Letters Vol. 83, Issue 10, p2386-2390, 2013. DOI: 10.1016/j.spl.2013.06.030
  59. Utility theory front to back - inferring utility from agents' choices. Co-authors: A.M.G. Cox and J. Obloj. arXiv:1101.3572 International Journal of Theoretical and Applied Finance 17 #3 May 2014. DOI 10.1142/S0219024914500186
  60. Gambling in Contests modelled with diffusions. Co-author: Han Feng. Decisions in Economics and Finance, 38, #1, p21-37. 2015. Online First
  61. Robust price bounds for the forward starting straddle. Co-author: M. Klimmek. Finance and Stochastics Vol 19, Issue 1, 189-214, 2015. arXiv:1304.2141. The final publication is available from Online First DOI: 10.1007/s00780-014-0249-4
  62. Integrability of solutions of the Skorokhod Embedding Problem for diffusions. Electronic J. Probability 20, #83 1-26, 2015. DOI:10.1214/EJP.v20-4121
  63. Finite, integrable and bounded time embeddings for diffusions. Co-authors S. Ankirchner and P.Strack. Bernoulli. 21(2), May 2015. 1067-1088 arXiv:1306.3942
  64. Gambling in contests with random initial law. Co-author Han Feng. arXiv:1405.7801 Annals of Applied Probability 26(1) 186-215 (2016)
  65. Mimicking martingales. arXiv:1505.03709 Annals of Applied Probability 26(4) 2273-2303 (2016) Published Version.
  66. Optimal consumption and sale strategies for a risk averse agent. Co-author Yeqi Zhu. arXiv:1409.3394 DOI:10.1137/140982738. SIAM J Financial Mathematics Vol 7, Issue 1 674-719 (2016) Published Version.
  67. Gambling in contests with regret. Co-author Han Feng. arXiv:1301.0719 Mathematical Finance 26(3) 674-695, 2016
  68. Model uncertainty and the pricing of American options. Co-author Anthony Neuberger. arXiv:1604.02269 Finance and Stochastics, 21, p285-329, 2017. DOI:10.1007/s00780-016-0314-2 Available from Online First.See also: More on the heging of American options under model uncertainty. Co-author Anthony Neuberger.arXiv:1604.02274
  69. Randomized Strategies and Prospect Theory in a Dynamic Context. Co-authors V.Henderson, A.Tse Journal of Economic Theory 168, 287-300. 2017. Journal vesrion. SSRN Working paper
  70. Optimal stopping and the sufficiency of randomized threshold strategies. Co-authors V.Henderson, M.Zeng.arXiv:1708.01038 Electronic Communications in Probability, 23(1) p1-11, 2018. DOI:10.1214/18-ECP125
  71. Probability Weighting, Stop-Loss and the Disposition Effect. Co-authors V.Henderson, A.Tse (First version August 2016.) SSRN Working paper (March 2017). Journal of Economic Theory, 178, p360-397, November 2018. DOI:10.1016/j.jet.2018.10.002
  72. Optimal consumption and investment under transaction costs. Co-auhors Alex S.L. Tse, Yeqi Zhu arXiv:1612.00720 Mathematical Finance, 29(2), 483-506, April 2019. DOI 10.1111/mafi.12187
  73. The left-curtain martingale coupling in the presence of atoms. Co-author D.Norgilas. arXiv:1802.08337 Annals of Applied Probability 29(3) 1904-1928, 2019. Euclid DOI:10.1214/18-AAP1450 Published version.
  74. Robust bounds for the American put. Co-author D. Norgilas arXiv:1711.06466 Finance and Stochastics 23, 359-395, 2019. Journal version DOI: 10.1007/s00780-019-00385-4 Journal link
  75. A multi-asset investment and consumption problem with transaction costs Co-authors: Alex S.L. Tse, Yeqi Zhu arXiv:1612:01327 Finance and Stochastics 23, 4641-676, 2019. DOI:10.1007/s00780-019-00391-6 Journal link (This is a modified and extended version of Multi-asset consumption investment problems with infinite transaction costs. Co-author Yeqi Zhu. arXiv:1409.8307)
  76. Randomised rules for stopping problems. Co-author: M.Zeng Preprint Journal of Applied Probability, 53, #3, 981-1004, 2020. DOI:10.1017/jpr.2020.43
  77. The shape of the value function under Poisson optimal stopping.arXiv:2003.03834 Stochastic Processes and Applications 133 229-246 March 2021 DOI:10.1016/j.spa.2020.12.001
  78. An elementary approach to the Merton problem. Co-authors M.Herdegen, J.Jerome. SSRN Working Paper (July 2020) Mathematical Finance 31, #4, 1218-1239, 2021
  79. The potential of the shadow measure. Co-authors M. Beiglboeck, D. Norgilas. ArXiV:2008.09936 Electronic Communications in Probability, Vol 27, Paper 16, 1-12, 2022. Final version
  80. Cautious stochastic choice, optimal stopping and deliberate randomization. Co-authors V.Henderson, M.Zeng. Economic Theory.(2022) DOI:10.1007/s00199-022-01428-2SSRN Working Paper (January 2018). Published version.
  81. Constrained optimal stopping, liquidity and effort. Co-author: M.Zeng arXiv:1901.07270 Stochastic Processes and Applications Vol 150 p819-843, 2022. DOI:10.1016/j.spa.2019.10.010
  82. A construction of the left-curtain coupling. Co-author D. Norgilas. ArXiV:2102.10549 Electronic Journal of Probability 27, 1-46, 2022. DOI: 10.1214/22-EJP868
  83. The infinite-horizon investment-consumption problem for Epstein-Zin stochastic differential utility. I Foundations. Co-authors: M. Herdegen, J. Jerome. ArXiV:2107.06593 Finance and Stochastics, 27, 127-158, 2023. DOI: 10.1007/s00780-022-00495-6
  84. The infinite horizon investment-consumption problem for Epstein-Zin stochastic differential utility. II Existence, uniqueness and verification for $\theta \in (0,1)$. Co-authors: M. Herdegen, J. Jerome. ArXiV:2107.06593 Finance and Stochastics, 27, 159-188, 2023. DOI: 10.1007/s00780-022-00496-5

Accepted Papers

  • Callable convertible bonds under liquidity constraints and hybrid priorities. Co-authors: Gechun Liang, Edward Wang. ArXiV:2111.02554 To appear in SIAM Journal on Financial Mathematics
  • Proper solutions for Epstein-Zin stochastic differential utility. Co-authors: M. Herdegen, J. Jerome. ArXiV:2112.06708 To appear in Finance and Stochastics

Submitted papers and preprints

  • When is recursive utility well founded? Co-authors: M. Herdegen, J. Jerome. SSRN Version
  • An injective martingale coupling. Co-author: D. Norgilas. ArXiV:2303.01578
  • Portfolio optimization under transaction costs with Recursive Preferences. Co-authors: M.Herdegen and A. Tse.SSRN Version. ArXiV:2402.08387
  • Zero-sum Dynkin games under common and independent Poisson constraints. Co-authors: G.Liang and Edward Wang. ArXiV:2411.07134

David Hobson's home page.

Page created: 31st January 2007.

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