IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/34083.html
   My bibliography  Save this paper

An anticipative Markov modulated market

Author

Listed:
  • D'Auria, Bernardo
  • Salmerón Garrido, José Antonio

Abstract

A Markovian modulation captures the trend in the market and influences the market coefficients accordingly. The different scenarios presented by the market are modeled as the distinct states of a discrete-time Markov chain. In our paper, we assume the existence of such modulation in a market and, as a novelty, we assume that it can be anticipative with respect to the future of the Brownian motion that drives the dynamics of the risky asset. By employing these own techniques of enlargement of filtrations, we solve an optimal portfolio utility problem in both a complete and an incomplete market. Many examples of anticipative Markov chains are presented for which we compute the additional gain of the investor who has a more accurate information

Suggested Citation

  • D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2022. "An anticipative Markov modulated market," DES - Working Papers. Statistics and Econometrics. WS 34083, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:34083
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/c72b0abb-89b9-48a0-98c9-8039bcabb35a/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fontana, Claudio, 2018. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1007-1033.
    2. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    3. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    4. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    5. Olivier Menoukeu Pamen, 2017. "Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 373-410, November.
    6. Peter Imkeller, 2003. "Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 153-169, January.
    7. Imkeller, Peter & Pontier, Monique & Weisz, Ferenc, 2001. "Free lunch and arbitrage possibilities in a financial market model with an insider," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 103-130, March.
    8. Jin, Zhuo & Liu, Guo & Yang, Hailiang, 2020. "Optimal consumption and investment strategies with liquidity risk and lifetime uncertainty for Markov regime-switching jump diffusion models," European Journal of Operational Research, Elsevier, vol. 280(3), pages 1130-1143.
    9. Hans‐Peter Bermin, 2002. "A General Approach to Hedging Options: Applications to Barrier and Partial Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 199-218, July.
    10. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption‐Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279, April.
    11. Oliveira, Carlos & Perkowski, Nicolas, 2020. "Optimal investment decision under switching regimes of subsidy support," European Journal of Operational Research, Elsevier, vol. 285(1), pages 120-132.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Traian Pirvu & Huayue Zhang, 2013. "Investment and Consumption with Regime-Switching Discount Rates," Papers 1303.1248, arXiv.org.
    2. Traian A. Pirvu & Huayue Zhang, 2011. "On Investment-Consumption with Regime-Switching," Papers 1107.1895, arXiv.org.
    3. Hu, Fengxia & Wang, Rongming, 2017. "Optimal investment–consumption strategy with liability and regime switching model under Value-at-Risk constraint," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 103-118.
    4. Pirvu, Traian A. & Zhang, Huayue, 2014. "Investment–consumption with regime-switching discount rates," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 142-150.
    5. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    6. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    7. Mengzhe Zhang & Leunglung Chan, 2016. "Saddlepoint approximations to option price in a regime-switching model," Annals of Finance, Springer, vol. 12(1), pages 55-69, February.
    8. Mengzhe Zhang & Leunglung Chan, 2016. "Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-20, December.
    9. Benjamín Vallejo Jiménez & Francisco Venegas Martínez, 2017. "Optimal consumption and portfolio rules when the asset price is driven by a time-inhomogeneous Markov modulated fractional Brownian motion with," Economics Bulletin, AccessEcon, vol. 37(1), pages 314-326.
    10. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption‐Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279, April.
    11. Michael C. Fu & Bingqing Li & Rongwen Wu & Tianqi Zhang, 2020. "Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model," Papers 2006.15054, arXiv.org.
    12. Salmerón Garrido, José Antonio & Nunno, Giulia Di & D'Auria, Bernardo, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," DES - Working Papers. Statistics and Econometrics. WS 35411, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Mauricio Elizalde & Carlos Escudero & Tomoyuki Ichiba, 2022. "Optimal investment with insider information using Skorokhod & Russo-Vallois integration," Papers 2211.07471, arXiv.org, revised Dec 2024.
    14. Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alexandru, 2011. "On pricing and hedging options in regime-switching models with feedback effect," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 694-713, May.
    15. Sakkas, E. & Le, H., 2009. "A Markov-modulated model for stocks paying discrete dividends," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 19-24, August.
    16. Abel Cadenillas & Ricardo Huamán-Aguilar, 2016. "Explicit formula for the optimal government debt ceiling," Annals of Operations Research, Springer, vol. 247(2), pages 415-449, December.
    17. Zou, Bin & Cadenillas, Abel, 2014. "Explicit solutions of optimal consumption, investment and insurance problems with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 159-167.
    18. Jér^me Detemple & Marcel Rindisbacher, 2005. "Closed‐Form Solutions For Optimal Portfolio Selection With Stochastic Interest Rate And Investment Constraints," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 539-568, October.
    19. Robert J. Elliott & Tak Kuen Siu, 2009. "Robust Optimal Portfolio Choice Under Markovian Regime-switching Model," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 145-157, June.
    20. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.

    More about this item

    Keywords

    Anticipative Information;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:34083. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.