Publications of L C G Rogers
1. `The interrelations between Moire patterns, contour
fringes, optical sufaces and their sum and difference effects' (with
G. L. Rogers), Optica Acta 24, 1977, 15--22.
2. `The probability that two samples in the plane will have
disjoint convex hulls' J. Appl. Probab. 15, 1978, 790--802.
3. `Markov functions' (with J. W. Pitman) Ann. Probab.
9, 1981, 573--582.
4. `Characterizing all diffusions with the 2M-X property'
Ann. Probab. 9, 1981, 561--572.
5. `Wiener-Hopf factorisation for matrices' (with M. T. Barlow
and D. Williams) Seminaire de Probabilites XIV, 1980, 324--331.
6. `Time substitution based on fluctuating additive functionals' (with D. Williams)
Seminaire de Probabilites XIV, 1980, 332--342.
7. `Williams' characterisation of the Brownian excursion law;
proof and applications' Seminaire de Probabilites XV, 1981, 227--249.
8. `Stochastic integrals: basic theory' Proceedings of the 1980
LMS Symposium on Stochastic Integrals, Springer LNM 851, 1981, 56--72.
9. `A martingale approach to some Wiener-Hopf problems I' (with
R. R. London, H. P. McKean, and D. Williams) Seminaire de Probabilites XVI, 1982, 41--67.
10. `A martingale approach to some Wiener-Hopf problems II' (with
R. R. London, H. P. McKean, and D. Williams) Seminaire de Probabilites XVI, 1982, 68--90.
11. `It\^o excursion theory via resolvents'
Z. Wahrscheinlichkeitsth. verw. Geb. 63, 1983,
237--255.
12. `Wiener-Hopf factorisation of diffusions and Levy
processes' Proc. London Math. Soc. 47, 1983, 177--191.
13. `A new identity for real Levy processes' Ann. Inst. Henri
Poincare 20, 1984, 21--34.
14. `A diffusion first passage problem' Seminar on
Stochastic Processes, 1983, 151--160. Birkhaeuser, Boston, 1984.
15. `The $k$-record processes are i.i.d..' (with C. M. Goldie)
Z. Wahrscheinlichkeitsth. verw. Geb.
67, 1984, 197--211.
16. `Recurrence of additive functionals of Markov chains'
Sankhya A 47, 47--56, 1985.
17. `Brownian local times and branching processes'
Seminaire de Probabilites XVIII,
1984, 42--55.
18. `Smooth transition densities for one-dimensional diffusions'
Bull. London Math. Soc. 17, 1985, 157--161.
19. `A differential equation in Wiener-Hopf theory' (with D.
Williams) Stochastic Analysis and its Applications, Springer
Lecture Notes 1095, 1984, 187--199.
20. `$BM(\bbbr^3)$ and its area integral $\int \beta \wedge
d\beta$' (with G. C. Price and D. Williams) Stochastic Analysis
and its Applications, Springer Lecture Notes 1095, 1984,
155--165.
21. `Coupling of multidimensional diffusion processes by
reflection' (with T. Lindvall) Ann. Probab. 14, 1986,
860--872.
22. `Characterizing one-dimensional diffusions using stochastic
calculus' Bull. London Math. Soc. 19, 1987, 183--185.
23. `Brownian motion of ellipsoids' (with J. R. Norris and D.
Williams) Trans. Amer. Math. Soc. 294, 1986, 757--765.
24. `Self-avoiding random walk: a Brownian motion model with
local time drift' (with J. R. Norris and D. Williams) Prob. Th.
and Rel. Fields 74, 1987, 271--287.
25. `Construction and approximation of transition matrix
functions' (with D. Williams) Analytic and Geometric
Stochastics, ed. D. G. Kendall, 1986, 133-160.
26. `Continuity of martingales in the Brownian excursion
filtration' Prob. Th. and Rel. Fields 76, 1987, 291--298.
27. `Skew-product decompositions of Brownian motions' (with E. J.
Pauwels) Contemporary Mathematics 73, AMS, Providence
R.I., 1988, 237--262.
28. `Local time and stochastic area integrals' (with
J. B. Walsh). Ann. Prob. 19, 1991, 457--483.
29. `The intrinsic local time sheet of Brownian motion' (with
J. B. Walsh). Prob. Th. Rel. Fields. 88, 1991, 363--379.
30. `Multiple points of Markov processes in a complete metric
space'. Seminaire de Probabilites, XXIII, 1989, 186-197.
31. `Coupling and the tail $\sigma$-field of a one-dimensional
diffusion' 78-88, Stochastic Calculus in Application (ed.
J.R. Norris) Longman, Harlow, 1988.
32. `A guided tour through excursions'. Bull. London
Math. Soc. 21, 1989, 305--341.
33. `Embedding optimal selection problems in a Poisson process'
(with F.T. Bruss). Stoch. Proc. Appl. 38, 1991, 267--278.
34. `Characterisation of Pascal process' (with F.T. Bruss).
Stoch. Procs. Appl. 37, 1991, 331--338.
35. `Statistical analysis of AES data from thin film growth
modes' (with G.E. Rhead). Thin Solid Films 188, 1990,
109--122.
36. `Brownian motion in a wedge with variable skew reflection'.
Trans. Amer. Math. Soc. 326, 1991, 227--236.
37. `Stochastic ordering of order statistics' (with A.D. Barbour
and T. Lindvall). J. Appl. Prob. 28, 1991,
278--286.
38. ` Brownian motion in a wedge with variable skew reflection
II'. Diffusion Processes and Related Problems in Analysis, Vol. 1
95--115, ed. M Pinsky. Birkhaeuser, Boston 1990.
39. `Summability methods and almost-sure convergence' (with N. H.
Bingham.) Almost-Everywhere
Convergence II, 69--83, ed. A. Bellow, R. L. Jones.
Academic Press, New York 1991.
40. `Limit theorems for transient diffusions on the line' (with
D. G. Hobson.) Prob. Th. Rel. Fields 89, 1991, 61--74.
41. `$A(t,B(t))$ is not a semimartingale' (with J. B. Walsh.)
Seminar on Stochastic Processes 1990, 275--283, eds. P. J. Fitzsimmons
and R. J. Williams. Birkhaeuser, Boston 1991.
42. `The exact 4/3 variation of a process arising from Brownian
motion'
(with J. B. Walsh.) Stochastics and Stochastics
Reports 51 , 1994, 267--291.
43. `Estimating variance from high, low and closing prices'
(with S. E. Satchell.)
Ann. Appl. Prob. 1, 1991, 504--512.
44. `Decomposing the branching Brownian path' (with K. M.
Jansons.) Ann. Appl. Prob. 2, 1992, 973--986.
45. `Asymptotic behaviour of Brownian polymers' (with R. T. Durrett.)
Prob. Th. Rel. Fields 92, 1992, 337--349.
46. `Probability theory and polymer physics' (with K. M.
Jansons.) J. Stat. Physics 65, 1991, 139--165.
47. `Probability and dispersion theory' (with K .M.
Jansons.) IMA J. Appl. Math. 55, 1995, 149--162.
48. `Equivalent martingale measures and no-arbitrage'.
Stochastics and Stochastics Reports 51, 1994, 41--49.
49. `On polymer conformations in elongational flows' (with T. Chan,
D. Dean, and K. M.
Jansons.) Comm. Math. Phys. 160, 1994, 239--257.
50. `Recurrence of two-dimensional drifting reflecting Brownian
motion in a quadrant' (with D. G. Hobson.) Math.
Proc. Cam. Phil. Soc. 113, 1993, 387--399.
51. `Quadratic functionals of Gaussian processes, optimal control,
and the ``Colditz" example' (with Z. Shi.) Stochastics and
Stochastics Reports 41, 1992, 201--218.
52. `Interacting Brownian particles and the Wigner law' (with Z. Shi.)
Prob. Th. Rel. Fields 95, 1993, 555--570.
53. `The estimation of the volatility of stock prices: a comparison
of some different methods that use high and low prices.' (with S. E. Satchell
and Y. Yoon.) Appl. Fin. Econ. 4, 1994, 241--247.
54. `The joint law of the maximum and the terminal value of a
martingale.' Prob. Th. Rel. Fields 95, 1993, 451--466.
55. `Are stock prices driven by the volume of trade?
Empirical analysis of the FT30, FT100 and certain British
shares over 1988--1990' (with S. E. Satchell and
Y.Yoon.) In Return Distributions in Finance, Knight, J. \& Satchell,
S. E., (editors), Butterworth-Heinemann, Oxford, 2001, 118--142
(ISBN = 0750647515).
56. `The harmonic functions of $(A_t,B_t)$.'
Math. Proc. Camb. Phil. Soc. 114, 1993, 369--377.
57. `Fluid models in queueing theory and Wiener-Hopf
factorisation of Markov chains.' Ann. Appl.
Prob. 4, 1994, 390--413.
58. `Computing the invariant law of a fluid model.'
(with Z. Shi.) J. Appl. Probability, 31 , 1994, 885--896.
59. `The value of an Asian option' (with Z.Shi.)
J. Appl. Probability, 32, 1995, 1077--1088.
60. `Time-reversal of the noisy Wiener-Hopf factorisation.'
Proc. Symposia Pure Math., 57, 129--135, American
Math. Soc., Providence RI, 1995.
61. `Which model for term-structure of interest rates should
one use?' Mathematical Finance, IMA Volume 65, 93--116, Springer,
New York, 1995.
62. `On coupling of random walks and Levy processes' (with T. Lindvall.)
J. Appl. Probability, 33, 1996, 122-126.
63. `Portfolio turnpikes' (with K. Back
and P. H. Dybvig.) Rev. Fin. Studies 12, 1999,165--195.
64. `A proof of Dassios' representation of the $\alpha$-quantile
of Brownian motion with drift' (with P. Embrechts and M. Yor.)
Ann. Appl. Probability 5, 1995, 757--767.
65. `Consistent fitting of one-factor models to interest
rate data' (with
W. Stummer.) Insurance Mathematics and Economics 27,
45--63, 2000.
66. `Complete models of stochastic volatility' (with
D. G. Hobson.) Mathematical Finance 8, 27--48, 1998.
67. `Recovery of preferences from observed portfolio
choice in a single realisation' (with P. H. Dybvig.)
Rev. Fin. Studies 10, 1997, 151--174.
68. `Gaussian errors.' RISK 9, January 1996, 42--45.
69. `Arbitrage from fractional Brownian motion'.
Mathematical Finance 7, 1997, 95--105.
70. `Volatility estimation with price quanta'.
Mathematical Finance 8, 1998, 277--290.
71. `The potential approach to the term structure of interest
rates and foreign exchange rates'. Mathematical Finance 7,
1997, 157--176.
72. `Fitting potential models to interest rates and
foreign exchange rates', (with O. Zane).
Vasicek and beyond, ed. L. P. Hughston, RISK Publications,
London 1997, 327--342.
73. `One for all'. RISK 10, 57--59, March 1997.
74. `Fast, accurate and inelegant valuation of American options',
(with A. Joubert.) In Numerical Methods in Finance, eds.
L. C. G. Rogers & D. Talay, 88--92,
Cambridge University Press, 1997.
75. `Fastest coupling of random walks'.
J. London Math. Soc. 60, 630--640, 2000
76. `Fast accurate binomial pricing of options' (with E. J. Stapleton.)
Finance and Stochastics 2, 3--17, 1998.
77. `Stochastic calculus and Markov methods'. In
Mathematics of Derivative Securities, M. A. H. Dempster
and S. R. Pliska, editors, 15--40, Cambridge University Press, 1997.
78. `Valuing moving barrier options' (with Omar Zane.)
J. Comp. Finance 1, 1997, 5--11.
79. `Saddle-point approximations to option prices' (with Omar Zane.)
Ann. Appl. Probability 9 , 493--503, 1999.
80. `The relaxed investor and parameter uncertainty'.
Finance & Stochastics 5, 131--154, 2001.
81. `A simple model of liquidity effects' (with Omar Zane).
In `Advances in Finance and Stochastics:
Essays in Honour of Dieter Sondermann', eds. K. Sandmann and
P. Schoenbucher, pp 161--176, Springer, Berlin, 2002
(IBSN = 3 540 43464 X).
82. `Designing and estimating models of high-frequency
data' (with Omar Zane). Preprint 1998.
83. `Volatility forecasting in a tick data model'.
In Forecasting Voaltility in the Financial Markets,
eds. J. L. Knight and S. E. Satchell, Butterworth-Heinemann,
Oxford, 1998
84. `Does the behaviour of the asset tell us anything about
the option price formula? A cautionary tale.' (with S. E. Satchell).
Appl. Financial Econ. 10, 2000, 37--39.
85. `Evaluating the optimal solution of
the Davis-Norman-Rishel problem' (with R. H. Stockbridge). In preparation.
86. `The origins of risk-neutral pricing and the Black-Scholes
formula.' In Handbook of Risk Management
and Analysis, ed. C. O. Alexander, Wiley, Chichester, 1998.
87. `Utility maximisation with time-lagged trading'
(with E. J. Stapleton). In `Computational Methods in Decision-Making,
Economics and Finance', eds. E.J. Kontoghiorghes, B. Rustem
and S. Siokos, pp 249--269, Kluwer, 2002 (ISBN = 1 4020 0839 2).
88. `The maximum maximum of a martingale constrained by an
intermediate law'
(with H. M. Brown and D. G. Hobson).
Probability Theory and Related Fields 119, 2001,
558--578.
89. `Robust hedging of barrier options'
(with H. M. Brown and D. G. Hobson).
Mathematical Finance 11, 2001, 285--314.
90. `Optimal stopping and embedding' (with D. Lamberton).
Journal of Applied Probability 37, 2000, 1143--1148.
91. `Evaluating first-passage probabilities for spectrally
one-sided Levy processes'.
Journal of Applied Probability 37, 2000, 1173-1180.
92. `Why is the effect of proportional transactions
costs $O(\delta^{2/3)$?', in Mathematics of Finance,
AMS Contemporary Mathematics Series, 351 ,
G. Yin and Q. Zhang (eds.), 2004, 303-308.
93. `Optimal capital structure and endogenous default'
(with B. Hilberink). Finance & Stochastics 6, 2002, 237--264.
94. `Markov chains and the potential approach to
modelling interest rates and exchange rates' (with
F. A. Yousaf). Mathematical Finance -
Bachelier Congress 2000,
ed. H. Geman, D. Madan, S. R. Pliska, \& T. Vorst, Springer 2002.
95. `Examining the effects of shocks to a market
equilibrium' (with
F. A. Yousaf). Preprint 2000.
96. `Large investors, takeovers and the rule of law'
(with J. P. Heritage). Monte Carlo
Methods and Applications 8, 2002, 357--370.
97. `Duality in optimal investment
and consumption problems with market frictions.' (with Irene Klein.)
Mathematical Finance 17 , 2007, 225--247.
98. `Monte Carlo valuation of American options.'
Mathematical Finance 12, 2002, 271--286.
99. `Duality in constrained optimal investment and consumption
problems: a synthesis'. Paris-Princeton Lectures on
Mathematical Finance 2002, (Springer Lecture Notes in
Mathematics 1814), 2003, 95--131.
100. `Two-sector stochastic growth models.' (with
P M Hartley). Australian Economic Papers 44, 2005, 322-351.
101. `The squared Ornstein-Uhlenbeck market.' (with J
Aquilina). Mathematical Finance 14, 2004, 487-513.
102. `Optimal exercise of American claims when markets are
not complete' (with J. Scheinkman). Preprint 2002.
103. `The Merton problem in an illiquid financial
market' (with S. Singh). In preparation.
104. `A very simple model of liquidity risk' (with U. Cetin).
In preparation.
105. `Perpetual defaultable callable convertible bonds'
(with J.P. Heritage and G. Leobacher). In preparation.
106. `Option pricing with Markov-modulated dynamics'
(with A. Jobert). SIAM Journal on Control and Optimization 44,
2006, 2063-2078.
107. `Equilibrium pricing with Markov-modulated dynamics'
(with G. di Graziano). Preprint.
108. `Stocks paying discrete dividends: modelling and
option pricing'
(with R. Korn). The Journal of Derivatives,
13, 2, 44-48, 2005.
109. `Equilibrium models for dependent defaults.' (with J
Aquilina). In preparation.
Books:
` Diffusions, Markov Processes and Martingales, Vol. 2' (with D.
Williams), Wiley, Chichester, 1987. (ISBN = 0 471 91482 7)
` Diffusions, Markov Processes and Martingales, Vol. 1'
(with D. Williams.) Wiley, Chichester, 1994. (ISBN = 0 471 95061 0)
` Numerical Methods in Finance' (edited jointly with Denis Talay).
Cambridge University Press, 1997. (ISBN = 0 521 57354 8)
Short notes:
1. `A simple proof of M\"untz's theorem' Math. Proc. Camb. Phil.
Soc. 90, 1981, 1--3.
2. `Addendum to "It\^o excursion theory via resolvents" '
Z. Wahrscheinlichkeitsth. verw. Geb.
67, 1984, 473--476.
3. `An excluded volume problem for Brownian motion' (with J. R.
Norris and D. Williams) Phys. Letters 112A, 1985, 16--18.
4. `Ignatov's theorem: an abbreviation of the proof of Engelen,
Tommassen and Vervaat' Adv. Appl. Prob. 21, 1989,
933--934.
5. `The two-sided exit problem for spectrally positive L\'evy
processes' J. Appl. Prob. 22, 1990, 486--487.
6. `The barrier sensitive tree' (with E. J. Stapleton.)
Derivatives Week, 8, No. 3, January 1999, 7--8.
7. `The relaxed investor'. RISK Magazine, January 1999.
Review Articles:
1. `Stochastic Differential Equations and Diffusion
Processes' by N. Ikeda and S. Watanabe. Bull. London Math.
Soc. 14, 1982, 449--450.
2. ` Stochastic calculus and its Applications' by R. J.
Elliott. Bull. London Math. Soc. 15, 1983, 526--528.
3. `Markov Chains', `Approximating Countable Markov
Chains', `Brownian Motion and Diffusion' by D. Freedman.
Bull. London Math. Soc. 16, 1984, 546--548.
4. `General Theory of Markov Processes' by M. J. Sharpe.
Bull. London Math. Soc. 21, 1989, 622--623.
5. `Probability: Theory and Examples' by R. T. Durrett.
Bull. London Math. Soc. 24, 1992, 205--204.