nach oben

Mathematics and Financial Economics

02.05.2024

A mean field game approach to relative investment–consumption games with habit formation

verfasst von: Zongxia Liang, Keyu Zhang

Erschienen in: Mathematics and Financial Economics

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

This paper studies an optimal investment–consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as benchmarks to evaluate the performance of her decision. We formulate the n-agent game problems and the corresponding mean field game problems under the two utilities. One mean field equilibrium is derived in a closed form in each problem. In each problem with n agents, an approximate Nash equilibrium is then constructed using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained. In addition, we provide some numerical illustrations of our results.

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

Nur mit Berechtigung zugänglich

Abel, A.B.: Asset prices under habit formation and catching up with the joneses. Am. Econ. Rev. 80(2), 38–42 (1990)MathSciNet

Abel, A.B.: Risk premia and term premia in general equilibrium. J. Monet. Econ. 43(1), 3–33 (1999). https://doi.org/10.1016/S0304-3932(98)00039-7CrossRef

Angoshtari, B., Bayraktar, E., Young, V.R.: Optimal consumption under a habit-formation constraint: the deterministic case. SIAM J. Financ. Math. 14(2), 557–597 (2023). https://doi.org/10.1137/22M1471560MathSciNetCrossRef

Bielagk, J., Lionnet, A., Dos Reis, G.: Equilibrium pricing under relative performance concerns. SIAM J. Financ. Math. 8(1), 435–482 (2017). https://doi.org/10.1137/16M1082536MathSciNetCrossRef

Bo, L., Wang, S., Yu, X.: A mean field game approach to equilibrium consumption under external habit formation. Preprint, available at arXiv:2206.13341 (2022)

Campbell, J.Y., Cochrane, J.H.: By force of habit: a consumption-based explanation of aggregate stock market behavior. J. Polit. Econ. 107(2), 205–251 (1999)CrossRef

Constantinides, G.M.: Habit formation: a resolution of the equity premium puzzle. J. Polit. Econ. 98(3), 519–543 (1990)CrossRef

Detemple, J.B., Zapatero, F.: Asset prices in an exchange economy with habit formation. Econometrica 59(6), 1633–1657 (1991)CrossRef

dos Reis, G., Platonov, V.: Forward utility and market adjustments in relative investment-consumption games of many players. SIAM J. Financ. Math. 13(3), 844–876 (2022). https://doi.org/10.1137/20M138421XMathSciNetCrossRef

10.

Espinosa, G.-E., Touzi, N.: Optimal investment under relative performance concerns. Math. Finance 25(2), 221–257 (2015). https://doi.org/10.1111/mafi.12034MathSciNetCrossRef

11.

Fernández-Villaverde, J., Krueger, D.: Consumption over the life cycle: facts from consumer expenditure survey data. Rev. Econ. Stat. 89(3), 552–565 (2007)CrossRef

12.

Guanxing, F.: Mean Field Portfolio Games with Consumption. Math. Financ. Econ. 17, 79–99 (2023). https://doi.org/10.1007/s11579-022-00328-2MathSciNetCrossRef

13.

Guanxing, F., Zhou, C.: Mean field portfolio games. Finance Stochast. 27, 189–231 (2023). https://doi.org/10.1007/s00780-022-00492-9MathSciNetCrossRef

14.

Gali, J.: Keeping up with the joneses: consumption externalities, portfolio choice, and asset prices. J. Money Credit Bank. 26(1), 1–8 (1994)CrossRef

15.

Gómez, J.-P.: The impact of keeping up with the joneses behavior on asset prices and portfolio choice. Finance Res. Lett. 4(2), 95–103 (2007). https://doi.org/10.1016/j.frl.2007.01.002CrossRef

16.

Hamaguchi, Y.: Time-inconsistent consumption-investment problems in incomplete markets under general discount functions. SIAM J. Control. Optim. 59(3), 2121–2146 (2021). https://doi.org/10.1137/19M1303782MathSciNetCrossRef

17.

Hu, R., Zariphopoulou, T.: N-player and mean-field games in itô-diffusion markets with competitive or homophilous interaction, pp. 209–237. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-98519-6_9

18.

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

19.

Lacker, D., Soret, A.: Many-player games of optimal consumption and investment under relative performance criteria. Math. Financ. Econ. 14, 263–281 (2020). https://doi.org/10.1007/s11579-019-00255-9MathSciNetCrossRef

20.

Lacker, D., Zariphopoulou, T.: Mean field and n-agent games for optimal investment under relative performance criteria. Math. Finance 29(4), 1003–1038 (2019). https://doi.org/10.1111/mafi.12206MathSciNetCrossRef

21.

Lasry, J.-M., Lions, P.-L.: Mean field games. Jpn. J. Math. 2, 229–260 (2007). https://doi.org/10.1007/s11537-007-0657-8MathSciNetCrossRef

22.

Liu, H.: Optimal consumption and investment with transaction costs and multiple risky assets. J. Finance 59(1), 289–338 (2004)CrossRef

23.

Ma, G., Zhu, S.-P.: Optimal investment and consumption under a continuous-time cointegration model with exponential utility. Quant. Finance 19(7), 1135–1149 (2019). https://doi.org/10.1080/14697688.2019.1570317MathSciNetCrossRef

24.

Merton, R.C.: Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econ. Stat. 51(3), 247–257 (1969)CrossRef

25.

Thurow, L.C.: The optimum lifetime distribution of consumption expenditures. Am. Econ. Rev. 59(3), 324–330 (1969)

26.

Vayanos, D.: Transaction costs and asset prices: a dynamic equilibrium model. Rev. Financ. Stud. 11(1), 1–58 (1998)CrossRef

Titel: A mean field game approach to relative investment–consumption games with habit formation
verfasst von: Zongxia Liang
Keyu Zhang
Publikationsdatum: 02.05.2024
Verlag: Springer Berlin Heidelberg
Erschienen in: Mathematics and Financial Economics
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-024-00360-4