Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Mathematics and Financial Economics

27.03.2024

Optimal bubble riding with price-dependent entry: a mean field game of controls with common noise

verfasst von: Ludovic Tangpi, Shichun Wang

Erschienen in: Mathematics and Financial Economics

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper we further extend the optimal bubble riding model proposed in Tangpi and Wang (Optimal bubble riding: a mean field game with varying entry times, 2022) by allowing for price-dependent entry times. Agents are characterized by their individual entry threshold that represents their belief in the strength of the bubble. Conversely, the growth dynamics of the bubble is fueled by the influx of players. Price-dependent entry naturally leads to a mean field game of controls with common noise and random entry time, for which we provide an existence result. The equilibrium is obtained by first solving discretized versions of the game in the weak formulation and then examining the measurability property in the limit. In this paper, the common noise comes from two sources: the price of the asset which all agents trade, and also the the exogenous bubble burst time, which we also discretize and incorporate into the model via progressive enlargement of filtration.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
2.
Ahuja, Saran: Wellposedness of mean field games with common noise under a weak monotonicity condition. SIAM J. Control Optim. 54(1), 30–48 (2016)MathSciNetCrossRef
3.
Akyildirim, E., Corbet, S., Cumming, D., Lucey, B., Sensoy, A.: Riding the wave of crypto-exuberance: the potential misusage of corporate blockchain announcements. Technol. Forecast. Soc. Change 159, 120191 (2020)CrossRef
4.
Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd edn. Springer, Cham (2006)
5.
Allen, F., Morris, S., Postlewaite, A.: Finite bubbles with short sale constraints and asymmetric information. J. Econ. Theory 61(2), 206–229 (1993)CrossRef
6.
Almgren, R., Chriss, N.: Optimal execution of portfolio transactions. J. Risk 3, 5–39 (2001)CrossRef
7.
8.
Azéma, J., Jeulin, T., Knight, F.B. Marc Y.: Le théorème d’arrêt en une fin d’ensemble prévisible. In: Séminaire de Probabilités XXVII, pp. 133–158. Springer, Berlin (1993)
9.
Bayraktar, E., Cecchin, A., Cohen, A., Delarue, F.: Finite state mean field games with wright–fisher common noise. Journal de Mathématiques Pures et Appliquées 147, 98–162 (2021)MathSciNetCrossRef
10.
Beaver, W.H.: The information content of annual earnings announcements. J. Account. Res. 6, 67–92 (1968)CrossRef
11.
Belfadli, R., Hamadéne, S., Ouknine, Y.: On one-dimensional stochastic differential equations involving the maximum process. Stoch. Dyn. 9(02), 277–292 (2009)MathSciNetCrossRef
12.
Blanchet-Scalliet, C., Jeanblanc, M.: Hazard rate for credit risk and hedging defaultable contingent claims. Finance Stoch. 8(1), 145–159 (2004)MathSciNetCrossRef
13.
Bouchaud, J.-P., Farmer, J.D., Lillo, F.: Chapter 2: How markets slowly digest changes in supply and demand? In: Thorsten, H., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution, Handbooks in Finance, pp. 57–160. North-Holland (2009)
14.
Burzoni, M., Campi, L.: Mean field games with absorption and common noise with a model of bank run. Stoch. Process. Appl. 164, 206–241 (2023)MathSciNetCrossRef
15.
Cardaliaguet, P.: Notes on mean field games. In: Technical Report, Université de Paris - Dauphine (2012)
16.
Cardaliaguet, P., Delarue, F., Lasry, J.-M., Lions, P.-L.: The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201). Princeton University Press, (2019). ISBN 9780691193717
17.
Carmona, R., Delarue, F.: Probabilistic Theory of Mean Field Games with Applications, vol. I. Springer, 1st edition (2018a)
18.
Carmona, R., Delarue, F.: Probabilistic Theory of Mean Field Games with Applictaions, vol. II. Springer, 1st edition (2018b)
19.
Carmona, R., Lacker, D.: A probabilistic weak formulation of mean field games and applications. Anna. Appl. Probab. 25(3), 1189–1231 (2015)MathSciNet
20.
Carmona, R., Delarue, F., Lacker, D.: Mean field games with common noise. Ann. Probab. 44(6), 3740–3803 (2016)MathSciNetCrossRef
21.
Cartea, A., Donnelly, R.F., Jaimungal, S.: Algorithmic trading with model uncertainty. SIAM J. Financ. Math. 8(1), 635–671 (2017)MathSciNetCrossRef
22.
Cheng, Stephanie F., De Franco, Gus, Jiang, Haibo, Lin, Pengkai: Riding the blockchain mania: public firms’ speculative 8-k disclosures. Manag. Sci. 65(12), 5901–5913 (2019)CrossRef
23.
Cohen, S.N., Elliott, R.J., Pearce, C.E.M.: A general comparison theorem for backward stochastic differential equations. Adv. Appl. Probab. 42(3), 878–898 (2010)MathSciNetCrossRef
24.
Credit Suisse Corporate Insights Group: The Investor Landscape: Four Evolving Themes and Their Implications. Technical Report, Credit Suisse, NY (2022)
25.
Delarue, F.: Restoring uniqueness to mean-field games by randomizing the equilibria. Stoch. Partial Differ. Equ. Anal. Comput. 7(4), 598–678 (2019)MathSciNet
26.
Delarue, F., Lacker, D., Ramanan, K.: From the master equation to mean field game limit theory: large deviations and concentration of measure. Ann. Probab. 48, 211–263 (2020)MathSciNetCrossRef
27.
Dellacherie, C., Maisonneuve, B., Paul-André M.: Probabilités et potentiel, chapitres XVII–XXIV, Processus de Markov (fin). Compléments de calcul stochastique, vol. 5. Hermann (1992)
28.
Djete, M.F.: Mean field games of controls: on the convergence of Nash equilibria. Ann. Appl. Probab. 33(4), 2824–2862 (2023)MathSciNetCrossRef
29.
Doblas-Madrid, A.: A robust model of bubbles with multidimensional uncertainty. Econometrica 80(5), 1845–1893 (2012)MathSciNetCrossRef
30.
31.
Pardoux, É.: Generalized discontinuous backward stochastic differential equations. In: El Karoui, N., Mazliak, L. (eds.) Backward Stochastic Differential Equations, Chapter IV, pp. 207–219. Addison Wesley Longman Limited (1997)
32.
Gangbo, W., Mészáros, A.R., Mou, C., Zhang, J.: Mean field games master equations with nonseparable hamiltonians and displacement monotonicity. Ann. Probab. 50(6), 2178–2217 (2022)MathSciNetCrossRef
33.
Griffin, J.M., Harris, J.H., Shu, T., Topaloglu, S.: Who drove and burst the tech bubble? J. Finance 66(4), 1251–1290 (2011)CrossRef
34.
Haussmann, U.G., Lepeltier, J.P.: On the existence of optimal controls. SIAM J. Control Optim. 28(4), 851–52 (1990)MathSciNetCrossRef
35.
Huang, M., Malhamé, R.P., Caines, P.E.: Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6(3), 221–252 (2006)MathSciNetCrossRef
36.
Huang, M., Caines, P.E., Malhame, R.P.: The Nash certainty equivalence principle and Mckean–Vlasov systems: an invariance principle and entry adaptation. In: 2007 46th IEEE Conference on Decision and Control, pp. 121–126 (2007)
37.
Jackson, J., Tangpi, L.: Quantitative convergence for displacement monotone mean field games with controlled volatility (2023)
38.
Jacod, J., Mémin, J.: Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité. Séminaire de probabilités de Strasbourg, Tome 15, 529–546 (1981)
39.
Johansen, A., Sornette, D., Ledoit, O.: Predicting financial crashes using discrete scale invariance. J. Risk 1(4), 5–32 (1999)CrossRef
40.
Johansen, A., Ledoit, O., Sornette, D.: Crashes at critical points. Int. J. Theor. Appl. Finance 3, 219–255 (2000)CrossRef
41.
Brunnermeier, M.K., Nagel, S.: Hedge funds and the technology bubble. J. Finance 59(5), 2013–2040 (2004)CrossRef
42.
Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, 2nd edn. Springer, New York (1991)
43.
El Karoui, N., Du, N.H., Jeanblanc-Picqué, M.: Compactification methods in the control of degenerate diffusions: existence of an optimal control. Stochastics 20(3), 169–219 (1987)MathSciNetCrossRef
44.
Kharroubi, I., Lim, T.: Progressive enlargement of filtrations and Backward SDEs with jumps. J. Theor. Probab. 27, 683–724 (2014)CrossRef
45.
Kurtz, T.: Weak and strong solutions of general stochastic models. Electron. Commun. Probab. 19, 1–16 (2014)MathSciNetCrossRef
46.
Lacker, D.: A general characterization of the mean field limit for stochastic differential games. Probab. Theory Relat. Fields 165(3), 581–648 (2016)MathSciNetCrossRef
47.
Lacker, D., Le Flem, L.: Closed-loop convergence for mean field games with common noise. Ann. Appl. Probab. 33(4), 2681–2733 (2023)MathSciNetCrossRef
48.
Lacker, D., Shkolnikov, M., Zhang, J.: Superposition and mimicking theorems for conditional Mckean Vlasov equations. J. Eur. Math. Soc. (2020)
49.
Lasry, J.-M., Lions, P.-L.: Jeux à champ moyen. I-le cas stationnaire. Comptes Rendus Mathematique 343(9), 619–625 (2006)
50.
Lasry, J.-M., Lions, P.-L.: Jeux à champ moyen. II-horizon fini et contrôle optimal. Comptes Rendus Mathematique 343(10), 679–684 (2006)MathSciNetCrossRef
51.
52.
Laurière, M., Tangpi, L.: Convergence of large population games to mean field games with interaction through the controls. SIAM J. Math. Anal. 54(3), 3535–3574 (2022)MathSciNetCrossRef
53.
Leal, L.S.: Topics in High-Frequency Optimal Execution and Microstructure of Product Repricings. Ph.D. thesis, Princeton University (2022)
54.
55.
Tóth, B., Mastromatteo, I., Bouchaud, J.P.: Anomalous impact in reaction-diffusion financial models. Phys. Rev. Lett. 113, 268701 (2014)CrossRef
56.
Mou, C., Zhang, J.: Mean field game master equations with anti-monotonicity conditions (2022)
57.
Pohl, M., Ristig, A., Schachermayer, W., Tangpi, L.: The amazing power of dimensional analysis: quantifying market impact. Market Microstruct. Liq. 3(3–4), 1850004 (2018)
58.
59.
60.
Sornette, D., Woodard, R., Yan, W., Zhou, W.-X.: Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model. Phys. A Stat. Mech. Appl. 392(19), 4417–4428 (2013)CrossRef
61.
Sotes-Paladino, J., Zapatero, F.: Riding the bubble with convex incentives. Rev. Financ. Stud. 32(4), 1416–1456 (2018)CrossRef
62.
63.
64.
Yamada, T., Watanabe, S.: On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11(1), 155–167 (1971)MathSciNet
65.
Yor, M.: Application d’un lemme de Jeulin au grossissement de la filtration brownienne. Séminaire de probabilités de Strasbourg 14, 189–199 (1980)MathSciNet
Metadaten
Titel
Optimal bubble riding with price-dependent entry: a mean field game of controls with common noise
verfasst von
Ludovic Tangpi
Shichun Wang
Publikationsdatum
27.03.2024
Verlag
Springer Berlin Heidelberg
Erschienen in
Mathematics and Financial Economics
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-024-00353-3