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Register a new userMean Field Portfolio Games in Incomplete Markets: Nonconstant Equilibria Do Not Exist in $L^infty$
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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 $L^infty$, and the constant equilibrium obtained in [21] is unique in $L^infty$, not only in the space of constant equilibria.
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Solar Renewable Energy Certificate (SREC) markets are a market-based system that incentivizes solar energy generation. A regulatory body imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a tradeable certificate for each MWh generated. Firms seek to navigate the market optimally by modulating their SREC generation and trading rates. As such, the SREC market can be viewed as a stochastic game, where agents interact through the SREC price. We study this stochastic game by solving the mean-field game (MFG) limit with sub-populations of heterogeneous agents. Market participants optimize costs accounting for trading frictions, cost of generation, non-linear non-compliance costs, and generation uncertainty. Moreover, we endogenize SREC price through market clearing. We characterize firms optimal controls as the solution of McKean-Vlasov (MV) FBSDEs and determine the equilibrium SREC price. We establish the existence and uniqueness of a solution to this MV-FBSDE, and prove that the MFG strategies form an $epsilon$-Nash equilibrium for the finite player game. Finally, we develop a numerical scheme for solving the MV-FBSDEs and conduct a simulation study.
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for the permanent impact they have on prices. This leads to a large stochastic game, where each agents performance criteria are computed under a different probability measure. We analyse the mean-field game (MFG) limit of the stochastic game and show that the Nash equilibrium is given by the solution to a non-standard vector-valued forward-backward stochastic differential equation. Under some mild assumptions, we construct the solution in terms of expectations of the filtered states. Furthermore, we prove the MFG strategy forms an $epsilon$-Nash equilibrium for the finite player game. Lastly, we present a least-squares Monte Carlo based algorithm for computing the equilibria and show through simulations that increasing disagreement may increase price volatility and trading activity.
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We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log-normal markets. We construct explicit constant equilibrium strategies for both the finite population games and the corresponding mean field games, which we show are unique in the class of constant equilibria. In the CARA case, competition drives agents to invest more in the risky asset than they would otherwise, while in the CRRA case competitive agents may over- or under-invest, depending on their levels of risk tolerance.
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