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Virtualconference

H 1 Optimizing dividends and limited capital injections via exponential approximations I

Auteurs : Avram, Florin (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The recent papers Gajek-Kucinsky (2017), Avram-Goreac-LiWu (2020) investigated the control problem of optimizing dividends when limiting capital injections by bankruptcy is taken into consideration. The first paper works under the spectrally negative Levy model; the second works under the Cramer-Lundberg model with exponential jumps, where the results are considerably more explicit.
    The first talk extends, exploiting the W-Z scale functions, results of Gajek-Kucinsky (2017) to the case when a final penalty is taken into consideration as well. This requires the introduction of new scale and Gerber-Shiu functions.
    The second talk illustrates the fact that quite reasonable approximations of the general problem may be obtained using the exponential particular case studied in Avram-Goreac-LiWu (2020). We start by experimenting with de Vylder type approximations for the scale function $W_q(x)$; this amounts essentially to replacing our process by one with exponential jumps and cleverly crafted parameters based on the first three moments of the claims. We show that very good approximations may be obtained for two fundamental objects of interest: the growth exponent $\Phi_q$ of the scale function $W_q(x)$, and the (last) global minimum of $W_q'(x)$, which is fundamental in the de Finetti barrier problem. Turning then to the dividends and limited capital injections problem, we show that a new exponential approximation specific to this problem achieves very good results: it consists in plugging into the objective function for exponential claims the exact "non-exponential ingredients" (scale functions and, survival and mean functions) of our non-exponential examples.

    Keywords : Lokka-Zervos-type alternative; optimal dividends; capital injections; buffered eflection; Cramer-Lundberg model; absolutely continuous supersolutions; scale functions

    Codes MSC :
    60G40 - Stopping times; optimal stopping problems; gambling theory
    60J35 - Transition functions, generators and resolvents
    60J75 - Jump processes


    Ressources complémentaires :
    https://www.cirm-math.com/uploads/2/6/6/0/26605521/avram_cirm.pdf


      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 02/11/2020
      Date de captation : 02/11/2020
      Collection : Research school ; Probability and Statistics
      Durée : 1:09:45
      Domaine : Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-10-28_Avram.mp4

    Informations sur la Rencontre Virtuelle

    Nom de la rencontre : Jean-Morlet Chair 2020 - Research School: Quasi-Monte Carlo Methods and Applications / Chaire Jean-Morlet 2020 - Ecole: Méthode de quasi-Monte-Carlo et applications
    Organisateurs de la rencontre : Rivat, Joël ; Thonhauser, Stefan ; Tichy, Robert
    Dates : 02/11/2020 - 07/11/2020
    Année de la rencontre : 2020
    URL Congrès : https://www.chairejeanmorlet.com/2255.html

    Citation Data

    DOI : 10.24350/CIRM.V.19663803
    Cite this video as: Avram, Florin (2020). Optimizing dividends and limited capital injections via exponential approximations I.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19663803
    URI : http://dx.doi.org/10.24350/CIRM.V.19663803


    Voir aussi

    Bibliographie

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    2. AVRAM, Florin, GOREAC, Dan, LI, Juan, et al. Equity Cost-Induced Dichotomy for Optimal Dividends in the Cramér-Lundberg Model. 2020. - https://hal.archives-ouvertes.fr/hal-02912757/

    3. AVRAM, Florin, GRAHOVAC, Danijel, et VARDAR-ACAR, Ceren. The $ W, Z $ scale functions kit for first passage problems of spectrally negative Levy processes, and applications to the optimization of dividends. arXiv preprint arXiv:1706.06841, 2017. - https://arxiv.org/abs/1706.06841

    4. AVRAM, Florin, HORVÁTH, Andras, PROVOST, Serge, et al. On the Padé and Laguerre–Tricomi–Weeks Moments Based Approximations of the Scale Function W and of the Optimal Dividends Barrier for Spectrally Negative Lévy Risk Processes. Risks, 2019, vol. 7, no 4, p. 121. - https://doi.org/10.3390/risks7040121

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