# Papers

Here are my papers, many of which are downloadable. Published versions may differ from what is available from this site.

1. Bruss, F.T. & Rogers, L.C.G. (2022). The $$1/e$$ strategy is suboptimal for the problem of best choice under no information. Stochastic Processes and their Applications, 150, 1059-1057.
2. Ernst, P.A., Kagan, A. & Rogers, L.C.G. (2022). The least favorable noise. Electronic Communications in Probability, 27, 1-11.
3. Rogers, L.C.G. (2020). Ending the COVID-19 epidemic in the United Kingdom. Preprint (arxiv 2004.12462). Jupyter notebook on Google Colab.
4. Rogers, L.C.G. (2019). Things we think we know. Preprint.
5. Rogers, L.C.G. (2018). Sense, nonsense and the S&P500. Decisions in Economics and Finance, 41, 447-461.
6. Ernst, P., Rogers, L.C.G. & Zhou, Q (2019). The distribution of Yule’s Nonsense correlation’. Submitted.
7. Ernst, P. and Rogers, L.C.G. (2019). The value of insight. To appear in Mathematics of Operations Research.
8. Ernst, P., Rogers, L.C.G. & Zhou, Q (2020). When is it best to follow the leader?  Stochastic Processes and their Applications, 130, 3394-3407.
9. Rogers, L.C.G. (2018). Combining different models. Mathematical Finance and Economics, 12, 97-109.
10. Ernst, P., Rogers, L.C.G. & Zhou, Q (2016). The value of foresight. Preprint, arxiv:1601.05872.
11. Rogers, L.C.G. (2015) Bermudan options by simulation. Preprint, arxiv:1508.06117.
12. Duembgen, M. & Rogers, L.C.G. (2015). The joint law of the extrema, signature, and final value of a stopped random walk. In Séminaire de Probabilités XLVII, 321-338. Preprint, arxiv:1403.0220.
13. Duembgen, M. & Rogers, L.C.G. (2014). Investing and stopping. Journal of Applied Probability, 51, 898-909, arxiv:1403.0202
14. Gonon, L. & Rogers, L.C.G. (2014). Evolution of firm size. International Journal of Theoretical and Applied Finance, 17.
15. Duembgen, M. & Rogers, L.C.G. (2014) Estimate nothing. Quantitative Finance, 14, 2065-2072, arxiv:1401.5666. T-shirt design here .
16. Rogers, L.C.G. & Zaczkowski, P. (2013). Monte Carlo approximation to optimal investment. Preprint, arxiv:1305.3433
17. Rogers, L.C.G. & Veraart, L.A.M (2013). Failure and rescue in an interbank network. Management Science 59, 882-898.
18. Muraviev, R. & Rogers, L.C.G. (2013). Utilities bounded below. Annals of Finance 9, 271-289.
19. Rogers, L.C.G. & Zaczkowski, P. (2012). Firms, banks and households. Handbook on Systemic Risk, editors J.-P. Fouque & J. Langsam, Cambridge University Press,  372-400.
20. Rogers, L.C.G. (2012). Least action filtering. arxiv:1301.5157.
21. Dybvig, P.H. & Rogers, L.C.G. (2013). High hopes and disappointment. Preprint.
22. Brown, A.A. & Rogers, L.C.G. (2012). Diverse beliefs. Stochastics 84, 683-703.
23. Nishide, K. & Rogers, L.C.G. (2011). Market selection: hungry misers and bloated bankrupts. Mathematics and Financial Economics 5, 47-66.
24. Imkeller, N. & Rogers, L.C.G. (2014). Trading to stops. SIAM Journal on Financial Mathematics 5, 753-781.
25. Rogers, L.C.G. & Zhang, L. (2011). An asset return model capturing stylized facts. Mathematics and Financial Economics 5, 101-119.
26. Kluge, T. & Rogers, L.C.G. (2012). The potential approach in practice. arxiv:1204.5718v1.
27. Brown, A.A. & Rogers, L.C.G. (2010). Heterogeneous beliefs with mortal agents. In Recent Advances in Financial Engineering 2009, editors M. Kijima, C. Hara, K. Tanaka, Y. Muromachi, World Scientific, Singapore.
28. Nishide, K. & Rogers, L.C.G. (2011). Optimal time to exchange two baskets. Journal of Applied Probability 48, 21-30.
29. Rogers, L.C.G. (2010). Dual valuation and hedging of Bermudan options. SIAM Journal on Financial Mathematics 1, 604-608.
30. Rogers, L.C.G. (2009). Optimal and robust contracts for a risk-constrained principal. Mathematics and Financial Economics 2, 151-171.
31. Li, Tianhui M.& Rogers, L.C.G. (2009). Lucas economy with trading constraints. Preprint. Revised version (30/6/2022)  here.
32. Rogers, L.C.G. & Veraart, L.A.M. (2008). A stochastic volatility alternative to SABR. Journal of Applied Probability 45, 1071-1085.
33. Rogers, L.C.G. & Tehranchi, M.R. (2010). Can the implied volatility move by parallel shifts? Finance and Stochastics 14, 235-248.
34. Rogers, L.C.G. & Shepp, L.A. (2006). The correlation of the maxima of correlated Brownian motions. Journal of Applied Probability 43, 880-883.
35. Rogers, L.C.G. & Zhou, F. (2008). Estimating correlation from high, low, opening and closing prices. Annals of Applied Probability 18, 813-823.
36. Rogers, L.C.G. (2006). One for all. In Progress in Industrial Mathematics at ECMI 2004, Springer, Berlin, 407-421.
37. Di Graziano, G. & Rogers, L.C.G. (2009). A dynamic approach to the modelling of correlation credit derivatives using Markov chains. International Journal of Theoretical and Applied Finance 12, 1-18.
38. Rogers, L.C.G. (2007). Pathwise stochastic optimal control. SIAM Journal on Control and Optimization 46, 1116-1132.
39. Korn, R. & Rogers, L.C.G. (2005). Stocks paying discrete dividends: modelling and option pricing. Journal of Derivatives 13, 2, 44-48.
40. Di Graziano, G. & Rogers, L.C.G. (2006). Barrier option pricing for assets with Markov-modulated dividends. Journal of Computational Finance 9, 75-87.
41. Jobert, A. & Rogers, L.C.G. (2008). Valuations and dynamic convex risk measures. Mathematical Finance 18, 1-22.
42. Di Graziano, G. & Rogers, L.C.G. (2009). Equity with Markov-modulated dividends. Quantitative Finance 9, 19-26.
43. Jobert, A. & Rogers, L.C.G. (2006). Option pricing with Markov-modulated dynamics. SIAM Journal on Control and Optimization 44, 2063-2078.
44. Cetin, U. & Rogers, L.C.G. (2007). Modelling liquidity effects in discrete time. Mathematical Finance 17, 15-29.
45. Rogers, L.C.G. & Singh, S. (2010). The cost of illiquidity and its effects on hedging. Mathematical Finance 20, 597-615.
46. Rogers, L.C.G. & Scheinkman, J. (2007). Optimal exercise of executive stock options. Finance and Stochastics 11, 375-372.
47. Aquilina, J. & Rogers, L.C.G. (2004). The squared Ornstein-Uhlenbeck market. Mathematical Finance 14, 487-513.
48. Hartley, P.M. & Rogers, L.C.G. (2005). Two-sector stochastic growth models. Australian Economic Papers 44, 322-351.
49. Rogers, L.C.G. (2003). Duality in constrained optimal investment and consumption problems: a synthesis. In Paris-Princeton Lectures on Mathematical Finance 2002, Lecture Notes in Mathematics 1814, Springer, Berlin, 95-131
50. Rogers, L.C.G. (2002). Monte Carlo valuation of American options. Mathematical Finance 17, 271-286.
51. Klein, I. & Rogers, L.C.G. (2007). Duality in optimal investment and consumption problems with market frictions. Mathematical Finance 17, 225-247.
52. Heritage, J.P. & Rogers, L.C.G. (2002). Large investors, takeovers and the rule of law. Monte Carlo Methods and Applications, 8, 357-370.
53. Rogers, L.C.G. & Yousaf, F.A. (2002). Markov chains and the potential approach to modelling interest rates and exchange rates. In Mathematical Finance – Bachelier Congress 2000, editors H. Geman, D. Madan, S.R. Pliska,  & T. Vorst, Springer.
54. Hilberink, B. & Rogers, L.C.G. (2002). Optimal capital structure and endogenous default. Finance and Stochastics 6, 237-264.
55. Rogers, L.C.G. (2004). Why is the effect of transaction costs $$\small O(\delta^{2/3})$$? In Mathematics of Finance, AMS Contemporary Mathematics Series 351, editors G. Yin & Q. Zhang, 303-308.
56. Rogers, L.C.G. (2000). Evaluating first-passage probabilities for spectrally one-sided Lévy processes. Journal of Applied Probability 37, 1173-1180.
57. Lamberton, D. & Rogers, L.C.G. (2000). Optimal stopping and embedding. Journal of Applied Probability 37, 1143-1148.
58. Brown, H.M., Hobson, D.J. & Rogers, L.C.G. (2001). Robust hedging of barrier options. Mathematical Finance 11, 285-314.
59. Brown, H.M., Hobson, D.J. & Rogers, L.C.G. (2001). The maximum maximum of a martingale constrained by an intermediate law. Probability Theory and Related Fields 119, 558-578.
60. Rogers, L.C.G. & Stapleton, E.J. (2002). Utility maximisation with time-lagged trading. In Computational Methods in Decision-Making, editors E.J. Kontoghiorghes, B. Rustem & S. Siokos. Kluwer, 249-269.
61. Rogers, L.C.G. (1998). The origins of risk-neutral pricing and the Black-Scholes formula. In Handbook of Risk Management and Analysis, editor C.O. Alexander, Wiley, Chichester.
62. Rogers, L.C.G. & Satchell, S.E. (2000). Does the behaviour of the asset tell us anything about the option price formula? A cautionary tale. Applied Financial Economics 10, 37-39.
63. Rogers, L.C.G. (1998). Volatility forecasting in a tick data model. In Forecasting Volatility in the Financial Markets, editors J.L. Knight and S.E. Satchell, Butterworth-Heinemann, Oxford.
64. Rogers, L.C.G. & Zane, O. (2002).  A simple model of liquidity effects. In Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann, editors K. Sandmann and P. Schoenbucher, Springer, Berlin, 161-176.
65. Rogers, L.C.G. (2001). The relaxed investor and parameter uncertainty. Finance and Stochastics 5, 131-154.
66. Rogers, L.C.G. & Zane, O. (1999). Saddle-point approximations to option prices. Annals of Applied Probability 9, 493-503.
67. Rogers, L.C.G. & Zane, O. (1997). Valuing moving barrier options. Journal of Computational Finance 1, 5-11.
68. Rogers, L.C.G. (1997). Stochastic calculus and Markov methods. In Mathematics of Derivative Securities, editors M.A.H. Dempster and S.R. Pliska, Cambridge University Press, Cambridge, 15-40.
69. Rogers, L.C.G. & Stapleton, E.J. (1998). Fast accurate binomial pricing of options. Finance and Stochastics 2, 3-17.
70. Rogers, L.C.G. (2000). Fastest coupling of random walks. Journal of the London Mathematical Society 60, 630-640.
71. Rogers, L.C.G. (1997). One for all. RISK 10, 57-59.
72. Joubert, A. & Rogers, L.C.G. (1997). Fast, accurate and inelegant pricing of American options. In Numerical Methods in Finance, editors L.C.G. Rogers and D. Talay, Cambridge University Press, Cambridge, 88-92.
73. Rogers, L.C.G. & Zane, O. (1997). Fitting potential models to interest rates and foreign exchange rates. In Vasicek and beyond, editor L.P. Hughston, Risk Publications, London, 327-342.
74. Rogers, L.C.G. (1997). The potential approach to the term structure of interest rates and foreign exchange rates. Mathematical Finance 7, 157-176.
75. Rogers, L.C.G. (1998). Volatility estimation with price quanta. Mathematical Finance 8, 277-290.
76. Rogers, L.C.G. (1997). Arbitrage from fractional Brownian motion. Mathematical Finance 7, 95-105.
77. Rogers, L.C.G. (1996). Gaussian errors. RISK 9, 42-45.
78. Dybvig, P.H. & Rogers, L.C.G. (1997). Recovery of preferences from observed portfolio choice in a single realisation. Review of Financial Studies 10, 151-174.
79. Hobson, D.G. & Rogers, L.C.G. (1998). Complete models of stochastic volatility. Mathematical Finance 8, 27-48.
80. Rogers, L.C.G. & Stummer, W. (2000). Consistent fitting of one-factor models to interest rate data. Insurance Mathematics and Economics 29, 45-63.
81. Embrechts, P., Rogers, L.C.G. & Yor, M. (1995). A proof of Dassios’ representation of the $$\small\alpha$$-quantile of Brownian motion with drift. Annals of Applied Probability 5, 757-767.
82. Back, K., Dybvig, P.H. & Rogers, L.C.G. (1999). Portfolio turnpikes. Review of Financial Studies 12, 165-195.
83. Lindvall, T. & Rogers, L.C.G. (1996). On coupling of random walks and Lévy processes. Journal of Applied Probability 33, 122-126.
84. Rogers, L.C.G (1995). Which model for term-structure of interest rates should one use? Mathematical Finance, IMA Volume 65,  Springer, New York, 129-135.
85. Rogers, L.C.G. (1995). Time-reversal of noisy Wiener-Hopf factorisation. Proceedings of Symposia in Pure Mathematics 57, American Mathematical Society, Providence, R.I., 129-135.
86. Rogers, L.C.G. & Shi, Z. (1995). The value of an Asian option. Journal of Applied Probability 32, 1077-1088.
87. Rogers, L.C.G. & Shi, Z. (1994). Computing the invariant law of a fluid model. Journal of Applied Probability 31, 885-896.
88. Rogers, L.C.G. (1994). Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains. Annals of Applied Probability 4, 390-413.
89. Rogers, L.C.G. (1993). The harmonic functions of $$\small (A_t,B_t)$$. Mathematical Proceedings of the Cambridge Philosophical Society 114, 369-377.
90. Rogers, L.C.G, Satchell, S.E. & Yoon, Y. (2001). Are stock prices driven by volume of trade? Empirical analysis of the FT30, FT100 and certain British shares over 1988-1990. In Return Distributions in Finance, editors J. Knight and S.E. Satchell, Butterworth-Heinemann, Oxford, 118-142.
91. Rogers, L.C.G. (1993). The joint law of the maximum and terminal value of a martingale. Probability Theory and Related Fields 95, 451-466.
92. Rogers, L.C.G, Satchell, S.E. & Yoon, Y. (1994). The estimation of the volatility of stock prices: a comparison of some different methods that use high and low prices. Applied Financial Economics 4, 241-247.
93. Rogers, L.C.G. & Shi, Z. (1993). Interacting Brownian particles and the Wigner law. Probability Theory and Related Fields 95, 555-570.
94. Rogers, L.C.G. & Shi, Z. (1992). Quadratic functionals of Gaussian processes, optimal control, and the Colditz’ example. Stochastics and Stochastics Reports 41, 201-218.
95. Hobson, D.G. & Rogers, L.C.G. (1993). Recurrence of two-dimensional drifting reflecting Brownian motion in a quadrant. Mathematical Proceedings of the Cambridge Philosophical Society 113, 387-399.
96. Chan, T., Dean, D., Jansons, K.M. & Rogers, L.C.G. (1994). On polymer conformations in elongational flows. Communications in Mathematical Physics 160, 239-257.
97. Rogers, L.C.G. (1994). Equivalent martingale measures and no-arbitrage. Stochastics and Stochastics Reports 51, 41-49.
98. Jansons, K.M. & Rogers, L.C.G. (1995). Probability and dispersion theory. IMA Journal of Applied Mathematics 55, 149-162.
99. Jansons, K.M. & Rogers, L.C.G. (1991). Probability theory and polymer physics. Journal of Statistical Physics 65, 139-165.
100. Durrett, R.T. & Rogers, L.C.G. (1992). Asymptotic behaviour of Brownian polymers. Probability Theory and Related Fields 92, 337-349.
101. Jansons, K.M. & Rogers, L.C.G. (1992). Decomposing the branching Brownian path. Annals of Applied Probability 2, 973-986.
102. Rogers, L.C.G. & Satchell, S.E. (1991). Estimating variance from high, low and closing prices. Annals of Applied Probability 1, 504-512.
103. Rogers, L.C.G. & Walsh, J.B (1994). The exact 4/3 variation of a process arising from Brownian motion. Stochastics and Stochastics Reports 51, 267-291.
104. Rogers, L.C.G. & Walsh, J.B (1991). $$\small A(t,B(t))$$ is not a semimartingale. In Seminar on Stochastic Processes 1990, editors P.J. Fitzsimmons & R.J.Williams, Birkhaüser, Boston, 275-283.
105. Hobson, D.G. & Rogers, L.C.G. (1991). Limit theorems for transient diffusions on the line. Probability Theory and Related Fields 89, 61-74.
106. Bingham, N.H. & Rogers, L.C.G. (1991). Summability methods and almost-sure convergence. In Almost-everywhere Convergence II, editors A. Bellow & R.L. Jones, Academic Press, New York, 69-83.
107. Rogers, L.C.G. (1990). Brownian motion in a wedge with variable skew reflection II. In Diffusion Processes and Related Problems in Analysis, Volume 1, editor M. Pinsky, Birkhaüser, Boston, 95-115.
108. Barbour, A.D., Lindvall, T. & Rogers, L.C.G. (1991). Stochastic ordering of order statistics. Journal of Applied Probability 28, 278-286.
109. Rogers, L.C.G. (1991). Brownian motion in a wedge with variable skew reflection. Transactions of the American Mathematical Society 326, 227-236.
110. Bruss, F.T. & Rogers, L.C.G. (1991). Embedding optimal selection problems in a Poisson process. Stochastic Processes and their Applications 38, 267-278.
111. Bruss, F.T. & Rogers, L.C.G. (1991). Characterisation of Pascal processes. Stochastic Processes and their Applications 37, 331-338.
112. Rogers, L.C.G. & Walsh, J.B. (1991). The intrinsic local time sheet of Brownian motion. Probability Theory and Related Fields 88, 363-379.
113. Rogers, L.C.G. & Walsh, J.B. (1991). Local time and stochastic area integrals. Annals of Probability 19, 457-483.
114. Rhead, G.E. & Rogers, L.C.G. (1990). Statistical analysis of AES data from thin film growth modes. Thin Solid Films 188, 109-122.
115. Rogers, L.C.G. (1989). The two-sided exit problem for spectrally positive Lévy processes. Journal of Applied Probability 22, 486-487.
116. Rogers, L.C.G. (1989). A guided tour through excursions. Bulletin of the London Mathematical Society 21, 305-341.
117. Rogers, L.C.G. (1989). Multiple points of Markov processes in a complete metric space. In Séminaire de Probabilités XXIII, 186-197.
118. Rogers, L.C.G.(1989). Ignatov’s theorem: an abbreviation of the proof of Engelen, Tommassen and Vervaat. Advances in Applied Probability 21, 933-934.
119. Rogers, L.C.G. (1988). Coupling and the tail $$\sigma$$-field of a one-dimensional diffusion. In Stochastic Calculus in Application, editor J.R. Norris, Longman, Harlow, 78-88.
120. Pauwels, E.J & Rogers, L.C.G. (1988). Skew-product decompositions of Brownian motions. In Contemporary Mathematics 73, American Mathematical Society, Providence, R.I., 237-262.
121. Rogers, L.C.G. (1987). Continuity of martingales in the Brownian excursion filtration. Probability Theory and Related Fields 76, 291-298.
122. Rogers, L.C.G. & Williams, D. (1986). Construction and approximation of transition matrix functions. In Analytic and Geometric Stochastics, editor D.G. Kendall, 133-160.
123. Norris, J.R., Rogers, L.C.G. & Williams, D. (1987). Self-avoiding random walk: a Brownian motion model with local time drift. Probability Theory and Related Fields 74, 271-287.
124. Norris, J.R., Rogers, L.C.G. & Williams, D. (1986). Brownian motion of ellipsoids. Transactions of the American Mathematical Society 294, 757-765.
125. Norris, J.R., Rogers, L.C.G. & Williams, D. (1985). An excluded volume problem for Brownian motion. Physics Letters A 112A, 16-18.
126. Rogers, L.C.G (1987). Characterizing one-dimensional diffusions using stochastic calculus. Bulletin of the London Mathematical Society 19, 183-185.
127. Lindvall, T. & Rogers, L.C.G. (1986). Coupling of multidimensional diffusion processes by reflection. Annals of Probability 14, 860-872.
128. Price, G.C., Rogers, L.C.G. & Williams, D. (1984). $$\small BM({\mathbb R}^3)$$ and its area integral $$\small \int \beta \wedge d\beta$$. In Stochastic Analysis and its Applications, Springer Lecture Notes 1095, 155-165.
129. Rogers, L.C.G.& Williams, D. (1984). A differential equation in Wiener-Hopf theory. In Stochastic Analysis and its Applications, Springer Lecture Notes 1095, 187-199.
130. Rogers, L.C.G. (1984). Addendum to `Ito excursion theory via resolvents’. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 67,473-476.
131. Rogers, L.C.G. (1985). Smooth transition densities for one-dimensional diffusions. Bulletin of the London Mathematical Society, 17, 157-161.
132. Rogers, L.C.G. (1985). Recurrence of additive functionals of Markov chains. Sankhya A 47, 47-56.
133. Rogers, L.C.G. (1984). Brownian local times and branching processes. In Séminaire de Probabilités XVIII, 42-55.
134. Goldie, C.M. & Rogers, L.C.G. (1984). The $$\small k$$-record processes are i.i.d. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 67, 197-211.
135. Rogers, L.C.G. (1984). A diffusion first passage problem. In Seminar on Stochastic Processes 1983, Birkhaüser, Boston, 151-160.
136. Rogers, L.C.G. (1984). A new identity for Lévy processes. Annales de l’Institut Henri Poincaré 20, 21-34.
137. Rogers, L.C.G. (1983). Wiener-Hopf factorisation of diffusions and Lévy processes. Proceedings of the London Mathematical Society 47, 177-191.
138. Rogers, L.C.G. (1983). Itô excursion theory via resolvents. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 63, 237-255.
139. London, R.R., McKean, H.P., Rogers, L.C.G. & Williams, D. (1982) A martingale approach to some Wiener-Hopf problems II. In Séminaire de Probabilités XVI, 68-90.
140. London, R.R., McKean, H.P., Rogers, L.C.G. & Williams, D. (1982) A martingale approach to some Wiener-Hopf problems I. In Séminaire de Probabilités XVI, 41-67.
141. Rogers, L.C.G. (1981). Stochastic integrals: basic theory. In Proceedings of the 1980 LMS symposium on Stochastic Integrals, 56-72.
142. Rogers, L.C.G. (1981). Williams’ characterisation of the Brownian excursion law: proof and applications. In Séminaire de Probabilités XV, 227-249.
143. Rogers, L.C.G. (1981). Characterizing all diffusions with the $$\small 2M-X$$ property. Annals of Probability 9, 561-572.
144. Pitman, J.W. & Rogers, L.C.G. (1981). Markov functions. Annals of Probability 9, 573-582.
145. Rogers, L.C.G. (1981). A simple proof of Müntz’s theorem. Mathematical Proceedings of the Cambridge Philosophical Society 90, 1-3.
146. Barlow, M.T., Rogers, L.C.G. & Williams, D. (1980). Wiener-Hopf factorisation for matrices. In Séminaire de Probabilités XIV, 324-331.
147. Rogers, L.C.G. & Williams, D. (1980). Time substitution based on fluctuating additive functionals. In Séminaire de Probabilités XIV, 332-342.
148. Rogers, L.C.G. (1978). The probability that two samples in the plane will have disjoint convex hulls. Journal of Applied Probability 15, 790-802.
149. Rogers, G.L. & Rogers, L.C.G. (1977). The interrelations between Moiré patterns, contour fringes, optical surfaces and their sum and difference effects. Optica Acta 24, 15-22.