Mean Field Exponential Utility Game: A Probabilistic Approach

Fu, Guanxing; Su, Xizhi; Zhou, Chao

doi:10.48550/arxiv.2006.07684

Cited by 9 publications

(15 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, [2, Assumption A.1(iii)] is satisfied. By [12,Lemma A.1], it can be verified that there exists a positive constant C 1 depending only on R, T , α, γ, σ, σ 0 and h, Z ō BMO and Z 0,ō BMO such that 2cJ 2 (•; z, z 0 , θ)…”

Section: 3mentioning

confidence: 99%

Mean Field Portfolio Games

Fu¹,

Zhou²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study mean field portfolio games in incomplete markets with random market parameters, where each player is concerned with not only her own wealth but also the relative performance to her competitors. We use the martingale optimality principle approach to characterize the unique Nash equilibrium in terms of a mean field FBSDE with quadratic growth, which is solvable under a weak interaction assumption. Motivated by the weak interaction assumption, we establish an asymptotic expansion result in powers of the competition parameter. When the market parameters do not depend on the Brownian paths, we get the Nash equilibrium in closed form. Moreover, when all the market parameters become time-independent, we revisit the games in [21] and our analysis shows that nonconstant equilibria do not exist in L ∞ , and the constant equilibrium obtained in [21] is unique in L ∞ , not only in the space of constant equilibria.

show abstract

Section: 3mentioning

confidence: 99%

Mean Field Portfolio Games

Fu¹,

Zhou²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In these works, the benchmark for a particular agent was taken to be an empirical average of the other palyers' terminal wealth, multiplied by a constant factor between 0 and 1 representing the sensitivity of this particular agent to their peers' performance. Such a utility maximization problem under relative performance concerns has since been explored extensively using various techniques, see for instance [21,22,32,23,31,26] and references therein for a small sample of works on the question. We also refer to [17,1,18] for more recent articles studying relative performance concerns through the lens of the forward criteria of Musiela and Zariphopoulou [39].…”

Section: Introductionmentioning

confidence: 99%

Optimal Investment in a Large Population of Competitive and Heterogeneous Agents

Tangpi¹,

Xuchen²

2022

Preprint

View full text Add to dashboard Cite

This paper studies a stochastic utility maximization game under relative performance concerns in finite agent and infinite agent settings, where a continuum of agents interact through a graphon (see definition below). We consider an incomplete market model in which agents have CARA utilities, and we obtain characterizations of Nash equilibria in both the finite agent and graphon paradigms. Under modest assumptions on the denseness of the interaction graph among the agents, we establish convergence results for the Nash equilibria and optimal utilities of the finite player problem to the infinite player problem. This result is achieved as an application of a general backward propagation of chaos type result for systems of interacting forward-backward stochastic differential equations, where the interaction is heterogeneous and through the control processes, and the generator is of quadratic growth. In addition, characterizing the graphon game gives rise to a novel form of infinite dimensional forward-backward stochastic differential equation of Mckean-Vlasov type, for which we provide well-posedness results. An interesting consequence of our result is the computation of the competition indifference capital, i.e., the capital making an investor indifferent between whether or not to compete.

show abstract

“…To our knowledge, N -player games and MFGs in Itô-diffusion market settings have not been considered before except in preprint [6]. Therein, the authors used the same asset specialization framework and same CARA preferences as in [12] but allowed for Itô-diffusion price dynamics.…”

Section: Introductionmentioning

confidence: 99%

$N$-player and Mean-field Games in Itô-diffusion Markets with Competitive or Homophilous Interaction

Hu¹,

Zariphopoulou²

2021

Preprint

View full text Add to dashboard Cite

In Itô-diffusion environments, we introduce and analyze N -player and common-noise mean-field games in the context of optimal portfolio choice in a common market. The players invest in a finite horizon and also interact, driven either by competition or homophily. We study an incomplete market model in which the players have constant individual risk tolerance coefficients (CARA utilities). We also consider the general case of random individual risk tolerances and analyze the related games in a complete market setting. This randomness makes the problem substantially more complex as it leads to (N or a continuum of) auxiliary "individual" Itô-diffusion markets. For all cases, we derive explicit or closed-form solutions for the equilibrium stochastic processes, the optimal state processes, and the values of the games.

show abstract

Mean Field Exponential Utility Game: A Probabilistic Approach

Cited by 9 publications

References 36 publications

Mean Field Portfolio Games

Mean Field Portfolio Games

Optimal Investment in a Large Population of Competitive and Heterogeneous Agents

$N$-player and Mean-field Games in Itô-diffusion Markets with Competitive or Homophilous Interaction

Contact Info

Product

Resources

About