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Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon

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  • Tahir Choulli
  • Emmanuel Lepinette

Abstract

In this paper, we consider the discrete-time setting, and the market model described by (S,F,T)$. Herein F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable assets, and T is an arbitrary random time whose occurrence might not be observable via F. Thus, we consider the larger flow G which incorporates F and makes T an observable random time. This framework covers the credit risk theory setting, the life insurance setting and the setting of employee stock option valuation. For the stopped model (S^T,G) and for various vulnerable claims, based on this model, we address the super-hedging pricing valuation problem and its intrinsic Immediate-Profit arbitrage (IP hereafter for short). Our first main contribution lies in singling out the impact of change of prior and/or information on conditional essential supremum, which is a vital tool in super-hedging pricing. The second main contribution consists of describing as explicit as possible how the set of super-hedging prices expands under the stochasticity of T and its risks, and we address the IP arbitrage for (S^T,G) as well. The third main contribution resides in elaborating as explicit as possible pricing formulas for vulnerable claims, and singling out the various informational risks in the prices' dynamics.

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  • Tahir Choulli & Emmanuel Lepinette, 2024. "Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon," Papers 2401.05713, arXiv.org.
    • Handle: RePEc:arx:papers:2401.05713
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    References listed on IDEAS

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    1. Manfred Schäl, 1999. "Martingale Measures and Hedging for Discrete-Time Financial Markets," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 509-528, May.
    2. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2020. "A martingale representation theorem and valuation of defaultable securities," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1527-1564, October.
    3. repec:dau:papers:123456789/12268 is not listed on IDEAS
    4. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    5. Meriam El Mansour & Emmanuel Lépinette, 2020. "Conditional Interior and Conditional Closure of Random Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 356-369, November.
    6. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128, January.
    7. Peter Carr & Vadim Linetsky, 2000. "The Valuation of Executive Stock Options in an Intensity-Based Framework," Review of Finance, European Finance Association, vol. 4(3), pages 211-230.
    8. Kabanov, Yuri & Lépinette, Emmanuel, 2013. "Essential supremum with respect to a random partial order," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 478-487.
    9. Sircar, Ronnie & Xiong, Wei, 2007. "A general framework for evaluating executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2317-2349, July.
    10. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Tahir Choulli & Sina Yansori, 2022. "Log-optimal and numéraire portfolios for market models stopped at a random time," Finance and Stochastics, Springer, vol. 26(3), pages 535-585, July.
    12. Alain BÉlanger & Steven E. Shreve & Dennis Wong, 2004. "A General Framework For Pricing Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 317-350, July.
    13. repec:dau:papers:123456789/9699 is not listed on IDEAS
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