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Exponential Hedging and Entropic Penalties

Citations

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Cited by:

  1. Teemu Pennanen, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
  2. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
  3. Jin Hyuk Choi & Kim Weston, 2021. "Endogenous noise trackers in a Radner equilibrium," Papers 2108.00973, arXiv.org, revised Jun 2022.
  4. Daniel Bartl, 2016. "Exponential utility maximization under model uncertainty for unbounded endowments," Papers 1610.00999, arXiv.org, revised Feb 2019.
  5. Bruno Bouchard & Johannes Muhle-Karbe, 2022. "Simple Bounds for Transaction Costs," Post-Print hal-01711371, HAL.
  6. Michail Anthropelos & Gordan Žitković, 2010. "Partial equilibria with convex capital requirements: existence, uniqueness and stability," Annals of Finance, Springer, vol. 6(1), pages 107-135, January.
  7. Gunther Leobacher & Philip Ngare, 2014. "Utility indifference pricing of derivatives written on industrial loss indexes," Papers 1404.0879, arXiv.org.
  8. Ying Hu & Gechun Liang & Shanjian Tang, 2017. "Utility maximization in constrained and unbounded financial markets: Applications to indifference valuation, regime switching, consumption and Epstein-Zin recursive utility," Papers 1707.00199, arXiv.org, revised Oct 2024.
  9. Alessandro Doldi & Marco Frittelli, 2020. "Entropy Martingale Optimal Transport and Nonlinear Pricing-Hedging Duality," Papers 2005.12572, arXiv.org, revised Sep 2021.
  10. Weidong Tian & Daisuke Yoshikawa, 2017. "Analyzing Equilibrium in Incomplete Markets with Model Uncertainty," International Review of Finance, International Review of Finance Ltd., vol. 17(2), pages 235-262, June.
  11. Virbickaitė, Audronė & Ausín, M. Concepción & Galeano, Pedro, 2016. "A Bayesian non-parametric approach to asymmetric dynamic conditional correlation model with application to portfolio selection," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 814-829.
  12. Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.
  13. René Caldentey & Martin Haugh, 2006. "Optimal Control and Hedging of Operations in the Presence of Financial Markets," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 285-304, May.
  14. Michael Mania & Revaz Tevzadze, 2008. "Backward Stochastic PDEs Related to the Utility Maximization Problem," ICER Working Papers - Applied Mathematics Series 07-2008, ICER - International Centre for Economic Research.
  15. Gordan Žitković, 2012. "An example of a stochastic equilibrium with incomplete markets," Finance and Stochastics, Springer, vol. 16(2), pages 177-206, April.
  16. Friedrich Hubalek & Carlo Sgarra, 2006. "Esscher transforms and the minimal entropy martingale measure for exponential Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 125-145.
  17. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
  18. Tsukasa Fujiwara, 2009. "The Minimal Entropy Martingale Measures for Exponential Additive Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 65-95, March.
  19. Michael Monoyios, 2012. "Malliavin calculus method for asymptotic expansion of dual control problems," Papers 1209.6497, arXiv.org, revised Oct 2013.
  20. Anastasia Ellanskaya & Lioudmila Vostrikova, 2013. "Utility maximisation and utility indifference price for exponential semi-martingale models with random factor," Papers 1303.1134, arXiv.org.
  21. Thorsten Rheinländer, 2005. "An entropy approach to the Stein and Stein model with correlation," Finance and Stochastics, Springer, vol. 9(3), pages 399-413, July.
  22. Leitner Johannes, 2007. "Pricing and hedging with globally and instantaneously vanishing risk," Statistics & Risk Modeling, De Gruyter, vol. 25(4), pages 311-332, October.
  23. Christoph Czichowsky & Walter Schachermayer, 2015. "Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion," Papers 1505.02416, arXiv.org, revised Aug 2016.
  24. Anastasis Kratsios, 2019. "Partial Uncertainty and Applications to Risk-Averse Valuation," Papers 1909.13610, arXiv.org, revised Oct 2019.
  25. Markus Hess, 2019. "Optimal Equivalent Probability Measures under Enlarged Filtrations," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 813-839, December.
  26. Keita Owari, 2011. "On Admissible Strategies in Robust Utility Maximization," Papers 1109.5512, arXiv.org, revised Mar 2012.
  27. Ma, Hanmin & Tian, Dejian, 2021. "Generalized entropic risk measures and related BSDEs," Statistics & Probability Letters, Elsevier, vol. 174(C).
  28. repec:dau:papers:123456789/5374 is not listed on IDEAS
  29. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
  30. Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2024. "On entropy martingale optimal transport theory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 1-42, June.
  31. Tahir Choulli & Jun Deng & Junfeng Ma, 2012. "How Non-Arbitrage, Viability and Num\'eraire Portfolio are Related," Papers 1211.4598, arXiv.org, revised Jun 2014.
  32. Xing, Hao, 2017. "Stability of the exponential utility maximization problem with respect to preferences," LSE Research Online Documents on Economics 57213, London School of Economics and Political Science, LSE Library.
  33. Lixin Wu & Min Dai, 2009. "Pricing jump risk with utility indifference," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 177-186.
  34. Hao Xing, 2012. "Stability of the exponential utility maximization problem with respect to preferences," Papers 1205.6160, arXiv.org, revised Sep 2013.
  35. Kim Weston, 2014. "Stability of Utility Maximization in Nonequivalent Markets," Papers 1410.0915, arXiv.org, revised Jun 2015.
  36. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
  37. Teemu Pennanen & Ari-Pekka Perkkiö, 2018. "Convex duality in optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 22(4), pages 733-771, October.
  38. Teemu Pennanen & Ari-Pekka Perkkio, 2016. "Convex duality in optimal investment and contingent claim valuation in illiquid markets," Papers 1603.02867, arXiv.org.
  39. Michail Anthropelos & Gordan Zitkovic, 2008. "On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets," Papers 0803.2198, arXiv.org.
  40. Tankov, Peter & Voltchkova, Ekaterina, 2009. "Asymptotic analysis of hedging errors in models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2004-2027, June.
  41. Mark Owen & Gordan Zitkovic, 2007. "Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing," Papers 0706.0478, arXiv.org, revised Sep 2007.
  42. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
  43. Ilhan, Aytaç & Jonsson, Mattias & Sircar, Ronnie, 2009. "Optimal static-dynamic hedges for exotic options under convex risk measures," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3608-3632, October.
  44. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
  45. Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
  46. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios," Papers 2204.12250, arXiv.org.
  47. Scott Robertson & Konstantinos Spiliopoulos, 2014. "Indifference pricing for Contingent Claims: Large Deviations Effects," Papers 1410.0384, arXiv.org, revised Feb 2016.
  48. Michail Anthropelos & Michael Kupper & Antonis Papapantoleon, 2018. "An Equilibrium Model for Spot and Forward Prices of Commodities," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 152-180, February.
  49. Czichowsky, Christoph & Schachermayer, Walter, 2017. "Portfolio optimisation beyond semimartingales: shadowprices and fractional Brownian motion," LSE Research Online Documents on Economics 67689, London School of Economics and Political Science, LSE Library.
  50. Jonas Blessing & Michael Kupper & Alessandro Sgarabottolo, 2024. "Discrete approximation of risk-based prices under volatility uncertainty," Papers 2411.00713, arXiv.org.
  51. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
  52. Bayraktar, Erhan & Kravitz, Ross, 2013. "Stability of exponential utility maximization with respect to market perturbations," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1671-1690.
  53. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
  54. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2018. "Optimal Investment, Demand and Arbitrage under Price Impact," Papers 1804.09151, arXiv.org, revised Dec 2018.
  55. T. Choulli & S. Alsheyab, 2024. "Linear reflected backward stochastic differential equations arising from vulnerable claims in markets with random horizon," Papers 2408.04758, arXiv.org.
  56. Kramkov, D. & Sîrbu, M., 2007. "Asymptotic analysis of utility-based hedging strategies for small number of contingent claims," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1606-1620, November.
  57. Monoyios, Michael, 2007. "The minimal entropy measure and an Esscher transform in an incomplete market model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1070-1076, June.
  58. Rheinlander, Thorsten & Steiger, Gallus, 2006. "The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models," LSE Research Online Documents on Economics 16351, London School of Economics and Political Science, LSE Library.
  59. Bruno Bouchard & Johannes Muhle-Karbe, 2018. "Simple Bounds for Transaction Costs," Working Papers hal-01711371, HAL.
  60. Bouchard, Bruno & Muhle-Karbe, Johannes, 2022. "Simple bounds for utility maximization with small transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 98-113.
  61. M. R. Grasselli & T. R. Hurd, 2004. "Indifference pricing and hedging in stochastic volatility models," Papers math/0404447, arXiv.org.
  62. Michail Anthropelos & Nikolaos E. Frangos & Stylianos Z. Xanthopoulos & Athanasios N. Yannacopoulos, 2008. "On contingent claims pricing in incomplete markets: A risk sharing approach," Papers 0809.4781, arXiv.org, revised Feb 2012.
  63. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2015. "The pricing of contingent claims and optimal positions in asymptotically complete markets," Papers 1509.06210, arXiv.org, revised Sep 2016.
  64. Michael Monoyios, 2010. "Utility-Based Valuation and Hedging of Basis Risk With Partial Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 519-551.
  65. Owari, Keita & 尾張, 圭太, 2008. "Robust Exponential Hedging and Indifference Valuation," Discussion Papers 2008-09, Graduate School of Economics, Hitotsubashi University.
  66. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062, August.
  67. Ulrich Horst & Michael Kupper & Andrea Macrina & Christoph Mainberger, 2013. "Continuous equilibrium in affine and information-based capital asset pricing models," Annals of Finance, Springer, vol. 9(4), pages 725-755, November.
  68. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Martingale Schrödinger bridges and optimal semistatic portfolios," Finance and Stochastics, Springer, vol. 27(1), pages 233-254, January.
  69. Bruno Bouchard & Johannes Muhle-Karbe, 2018. "Simple Bounds for Utility Maximization with Small Transaction Costs," Papers 1802.06120, arXiv.org, revised Mar 2021.
  70. Tak Siu, 2006. "Option Pricing Under Autoregressive Random Variance Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 62-75.
  71. Thorsten Rheinländer & Gallus Steiger, 2010. "Utility Indifference Hedging with Exponential Additive Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(2), pages 151-169, June.
  72. Dmitry Kramkov & Kim Weston, 2015. "Muckenhoupt's $(A_p)$ condition and the existence of the optimal martingale measure," Papers 1507.05865, arXiv.org.
  73. Tsukasa Fujiwara, 2004. "From the Minimal Entropy Martingale Measures to the Optimal Strategies for the Exponential Utility Maximization: the Case of Geometric Lévy Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(4), pages 367-391, December.
  74. Keita Owari, 2011. "ON ADMISSIBLE STRATEGIES IN ROBUST UTILITY MAXIMIZATION(Revised in March 2012, Forthcoming in "Mathematics and Financial Economics")," CARF F-Series CARF-F-257, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  75. Johannes Leitner, 2008. "Convex pricing by a generalized entropy penalty," Papers 0804.0127, arXiv.org.
  76. N. Reich & C. Schwab & C. Winter, 2010. "On Kolmogorov equations for anisotropic multivariate Lévy processes," Finance and Stochastics, Springer, vol. 14(4), pages 527-567, December.
  77. Victor Richmond R. Jose & Robert F. Nau & Robert L. Winkler, 2008. "Scoring Rules, Generalized Entropy, and Utility Maximization," Operations Research, INFORMS, vol. 56(5), pages 1146-1157, October.
  78. Claudia Ceci & Anna Gerardi, 2011. "Utility indifference valuation for jump risky assets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(2), pages 85-120, November.
  79. Marina Santacroce & Paola Siri & Barbara Trivellato, 2023. "Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models," Papers 2302.08253, arXiv.org.
  80. Stephane Goutte & Armand Ngoupeyou, 2012. "Optimization problem and mean variance hedging on defaultable claims," Papers 1209.5953, arXiv.org.
  81. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
  82. Tetsuya Ishikawa & Scott Robertson, 2017. "Optimal Investment and Pricing in the Presence of Defaults," Papers 1703.00062, arXiv.org.
  83. Dejian Tian, 2022. "Pricing principle via Tsallis relative entropy in incomplete market," Papers 2201.05316, arXiv.org, revised Oct 2022.
  84. Kramkov, Dmitry & Weston, Kim, 2016. "Muckenhoupt’s (Ap) condition and the existence of the optimal martingale measure," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2615-2633.
  85. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2005. "A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation," Review of Derivatives Research, Springer, vol. 8(1), pages 5-25, June.
  86. Scott Robertson, 2012. "Pricing for Large Positions in Contingent Claims," Papers 1202.4007, arXiv.org, revised Dec 2013.
  87. Shuoqing Deng & Xiaolu Tan & Xiang Yu, 2020. "Utility Maximization with Proportional Transaction Costs Under Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1210-1236, November.
  88. Misumi, Takashi & 三隅, 隆司 & Nakamura, Hisashi & 中村, 恒 & Takaoka, Koichiro & 高岡, 浩一郎, 2014. "Moral-Hazard Premium," Working Paper Series G-1-7, Hitotsubashi University Center for Financial Research.
  89. Gordan Zitkovic, 2009. "An example of a stochastic equilibrium with incomplete markets," Papers 0906.0208, arXiv.org, revised Jun 2010.
  90. Kim Weston, 2022. "Existence of an equilibrium with limited participation," Papers 2206.12399, arXiv.org.
  91. Kohlmann, Michael & Niethammer, Christina R., 2007. "On convergence to the exponential utility problem," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1813-1834, December.
  92. Kuhn, Christoph, 2002. "Pricing contingent claims in incomplete markets when the holder can choose among different payoffs," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 215-233, October.
  93. Scott Robertson, 2023. "Equilibrium with Heterogeneous Information Flows," Papers 2304.01272, arXiv.org, revised Mar 2024.
  94. Alet Roux & Zhikang Xu, 2019. "Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs," Papers 1909.06260, arXiv.org, revised May 2021.
  95. Michail Anthropelos & Gordan Zitkovic, 2009. "Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability," Papers 0901.3318, arXiv.org.
  96. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
  97. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.
  98. Michael Ludkovski & Qunying Shen, 2012. "European Option Pricing with Liquidity Shocks," Papers 1205.1007, arXiv.org.
  99. Laurence Carassus & Miklós Rásonyi, 2011. "Risk-averse asymptotics for reservation prices," Annals of Finance, Springer, vol. 7(3), pages 375-387, August.
  100. Daniel Bartl & Patrick Cheridito & Michael Kupper, 2017. "Robust expected utility maximization with medial limits," Papers 1712.07699, arXiv.org, revised Nov 2018.
  101. Ludovic Tangpi & Xuchen Zhou, 2022. "Optimal Investment in a Large Population of Competitive and Heterogeneous Agents," Papers 2202.11314, arXiv.org, revised Feb 2023.
  102. Tahir Choulli & Jun Deng & Junfeng Ma, 2015. "How non-arbitrage, viability and numéraire portfolio are related," Finance and Stochastics, Springer, vol. 19(4), pages 719-741, October.
  103. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
  104. M. R. Grasselli & T. R. Hurd, 2007. "Indifference Pricing and Hedging for Volatility Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 303-317.
  105. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
  106. Laurence Carassus & Miklós Rásonyi, 2006. "Convergence of Utility Indifference Prices to the Superreplication Price," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 145-154, August.
  107. Gregor Heyne & Michael Kupper & Ludovic Tangpi, 2016. "Portfolio Optimization Under Nonlinear Utility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
  108. Kuhn, Christoph, 2004. "Game contingent claims in complete and incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 889-902, December.
  109. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2003. "A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation," OFRC Working Papers Series 2003mf02, Oxford Financial Research Centre.
  110. Kallsen Jan & Rheinländer Thorsten, 2011. "Asymptotic utility-based pricing and hedging for exponential utility," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 17-36, March.
  111. Keita Owari, 2011. "A Note on Utility Maximization with Unbounded Random Endowment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(1), pages 89-103, March.
  112. Romain Blanchard & Laurence Carassus, 2021. "Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 366-398, January.
  113. Romain Blanchard & Laurence Carassus, 2017. "Convergence of utility indifference prices to the superreplication price in a multiple-priors framework," Papers 1709.09465, arXiv.org, revised Oct 2020.
  114. Cl'ement M'enass'e & Peter Tankov, 2015. "Asymptotic indifference pricing in exponential L\'evy models," Papers 1502.03359, arXiv.org, revised Feb 2015.
  115. Shuoqing Deng & Xiaolu Tan & Xiang Yu, 2018. "Utility maximization with proportional transaction costs under model uncertainty," Papers 1805.06498, arXiv.org, revised Aug 2019.
  116. Klebert Kentia & Christoph Kuhn, 2017. "Nash equilibria for game contingent claims with utility-based hedging," Papers 1707.09351, arXiv.org, revised Sep 2018.
  117. Paolo Guasoni & Lóránt Nagy & Miklós Rásonyi, 2021. "Young, timid, and risk takers," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1332-1356, October.
  118. Wang, Nan, 2007. "Optimal investment for an insurer with exponential utility preference," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 77-84, January.
  119. Jan Kallsen & Johannes Muhle-Karbe, 2012. "Option Pricing and Hedging with Small Transaction Costs," Papers 1209.2555, arXiv.org, revised Dec 2012.
  120. Hurd T. R., 2004. "A note on log-optimal portfolios in exponential Lévy markets," Statistics & Risk Modeling, De Gruyter, vol. 22(3), pages 225-233, March.
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