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The value of partial information

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  • Philip A. Ernst
  • Oleksii Mostovyi

Abstract

We investigate a pricing rule that is applicable for streams of income or contingent claim liabilities and study how this rule changes under additional insider-type information that an investor might obtain. Considering a model where the risky asset might have jumps, we obtain an explicit form of the associated state price density for the three different types of agents considered in [ER20]: one who has no information about the jumps, one who knows in advance exactly when the each jump will occur, and one who has no information about the size of the jumps but has partial information about the size of each jump. For each of these agents, we provide characterizations of the pricing rule and establish a representation formula, allowing us to quantify the value of partial information for streams of labor income or contingent claim liabilities. Our work is motivated by finding and characterizing a pricing rule that, both with or without partial information about jumps, assigns different values of information for different income streams or contingent claim liabilities.

Suggested Citation

  • Philip A. Ernst & Oleksii Mostovyi, 2025. "The value of partial information," Papers 2505.08943, arXiv.org.
    • Handle: RePEc:arx:papers:2505.08943
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    References listed on IDEAS

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    1. Cetin, Umut & Danilova, Albina, 2021. "On pricing rules and optimal strategies in general Kyle-Back models," LSE Research Online Documents on Economics 113003, London School of Economics and Political Science, LSE Library.
    2. Albina Danilova & Michael Monoyios & Andrew Ng, 2009. "Optimal investment with inside information and parameter uncertainty," Papers 0911.3117, arXiv.org, revised Feb 2010.
    3. Ernst, Philip A. & Rogers, L.C.G. & Zhou, Quan, 2017. "The value of foresight," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3913-3927.
    4. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1761-1784.
    5. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," LSE Research Online Documents on Economics 65150, London School of Economics and Political Science, LSE Library.
    6. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
    7. Jin Hyuk Choi & Kookyoung Han, 2023. "Delegation of information acquisition, information asymmetry, and outside option," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 833-860, September.
    8. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2018. "No-arbitrage under a class of honest times," Finance and Stochastics, Springer, vol. 22(1), pages 127-159, January.
    9. Oleksii Mostovyi, 2017. "Optimal Investment With Intermediate Consumption And Random Endowment," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 96-114, January.
    10. Stefan Ankirchner & Steffen Dereich & Peter Imkeller, 2005. "The Shannon information of filtrations and the additional logarithmic utility of insiders," Papers math/0503013, arXiv.org, revised May 2006.
    11. Luciano Campi & Umut Çetin, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Finance and Stochastics, Springer, vol. 11(4), pages 591-602, October.
    12. Detemple, Jerome & Rindisbacher, Marcel & Robertson, Scott, 2022. "Dynamic noisy rational expectations equilibrium with insider information: Welfare and regulation," Journal of Economic Dynamics and Control, Elsevier, vol. 141(C).
    13. Philip A. Ernst & L. C. G. Rogers, 2020. "The Value of Insight," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1193-1209, November.
    14. Julien Hugonnier & Dmitry Kramkov & Walter Schachermayer, 2005. "On Utility‐Based Pricing Of Contingent Claims In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 203-212, April.
    15. Yuri Kabanov & Constantinos Kardaras & Shiqi Song, 2016. "No arbitrage of the first kind and local martingale numéraires," Finance and Stochastics, Springer, vol. 20(4), pages 1097-1108, October.
    16. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    17. Huy N. Chau & Andrea Cosso & Claudio Fontana & Oleksii Mostovyi, 2015. "Optimal investment with intermediate consumption under no unbounded profit with bounded risk," Papers 1509.01672, arXiv.org, revised Jun 2017.
    18. Koichiro Takaoka & Martin Schweizer, 2014. "A note on the condition of no unbounded profit with bounded risk," Finance and Stochastics, Springer, vol. 18(2), pages 393-405, April.
    19. Anna Aksamit & Tahir Choulli & Jun Deng & Monique Jeanblanc, 2017. "No-arbitrage up to random horizon for quasi-left-continuous models," Finance and Stochastics, Springer, vol. 21(4), pages 1103-1139, October.
    20. Umut c{C}etin & Hao Xing, 2012. "Point process bridges and weak convergence of insider trading models," Papers 1205.4358, arXiv.org, revised Jan 2013.
    21. Kardaras, Constantinos, 2010. "The continuous behavior of the numéraire portfolio under small changes in information structure, probabilistic views and investment constraints," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 331-347, March.
    22. repec:dau:papers:123456789/4436 is not listed on IDEAS
    23. Jan Kallsen, 2000. "Optimal portfolios for exponential Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 357-374, August.
    24. Huy N. Chau & Andrea Cosso & Claudio Fontana, 2020. "The value of informational arbitrage," Finance and Stochastics, Springer, vol. 24(2), pages 277-307, April.
    25. Sebastian Jaimungal & Xiaofei Shi, 2024. "The Price of Information," Papers 2402.11864, arXiv.org, revised Mar 2024.
    26. Cetin, Umut & Xing, Hao, 2013. "Point process bridges and weak convergence of insider trading models," LSE Research Online Documents on Economics 48745, London School of Economics and Political Science, LSE Library.
    27. Pietro Siorpaes, 2015. "Optimal investment and price dependence in a semi-static market," Finance and Stochastics, Springer, vol. 19(1), pages 161-187, January.
    28. Jerome Detemple & Marcel Rindisbacher & Scott Robertson, 2020. "Dynamic Noisy Rational Expectations Equilibrium With Insider Information," Econometrica, Econometric Society, vol. 88(6), pages 2697-2737, November.
    29. Çetin, Umut & Danilova, Albina, 2016. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," LSE Research Online Documents on Economics 63259, London School of Economics and Political Science, LSE Library.
    30. Oleksii Mostovyi, 2015. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Finance and Stochastics, Springer, vol. 19(1), pages 135-159, January.
    31. Robert J. Elliott & Monique Jeanblanc, 1999. "Incomplete markets with jumps and informed agents," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 475-492, December.
    32. Umut c{C}etin & Albina Danilova, 2014. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," Papers 1407.2420, arXiv.org, revised Sep 2016.
    33. Umut c{C}etin & Albina Danilova, 2018. "On pricing rules and optimal strategies in general Kyle-Back models," Papers 1812.07529, arXiv.org, revised Aug 2021.
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