Competition in Fund Management and Forward Relative Performance Criteria

Anthropelos, Michail; Geng, Tianran; Zariphopoulou, Thaleia

doi:10.2139/ssrn.3723229

Cited by 8 publications

(11 citation statements)

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“…For the exponential case, the MFG problem is to find a pair π * , X with the following properties. The investment strategy π * optimizes, in analogy to (2)…”

Section: Introductionmentioning

confidence: 99%

Mean field and n‐agent games for optimal investment under relative performance criteria

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Zariphopoulou

2019

Mathematical Finance

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134

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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 underinvest, depending on their levels of risk tolerance.

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“…For the exponential case, the MFG problem is to find a pair π * , X with the following properties. The investment strategy π * optimizes, in analogy to (2)…”

Section: Introductionmentioning

confidence: 99%

Mean field and n‐agent games for optimal investment under relative performance criteria

Lacker

Zariphopoulou

2019

Mathematical Finance

Self Cite

134

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“…That is, out-performing other fund managers tends to attract greater future investment in one's own fund. The most closely related works to ours, after [21], are [2,3,5,11,12,14]. These papers study continuous-time models of optimal investment under relative performance concerns in various settings, including different kinds of utilities, equilibrium pricing, and state constraints, but none incorporate consumption.…”

Section: Introductionmentioning

confidence: 99%

Many-player games of optimal consumption and investment under relative performance criteria

Lacker

Soret

2020

Math Finan Econ

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We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and consumption when compared to the averages among the other agents. We derive a closed form solution for the n-player game and the corresponding mean field game. This solution is unique in the class of equilibria with constant investment and continuous time-dependent consumption, both independent of the wealth of the agent. Compared to the classical Merton problem with one agent, the competitive model exhibits a wide range of highly nonlinear and non-monotone dependence on the agents' risk tolerance and competitiveness parameters. Counter-intuitively, competitive agents with high risk tolerance may behave like noncompetitive agents with low risk tolerance.

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“…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]. As in [20], [21,22,23] approach the problem from a purely probabilistic perspective through characterizing the game using systems of (forward) backward stochastic differential equation (F)BSDEs.…”

Section: Introductionmentioning

confidence: 99%

Optimal Investment in a Large Population of Competitive and Heterogeneous Agents

Tangpi¹,

Xuchen²

2022

Preprint

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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.

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Competition in Fund Management and Forward Relative Performance Criteria

Cited by 8 publications

References 0 publications

Mean field and n‐agent games for optimal investment under relative performance criteria

Mean field and n‐agent games for optimal investment under relative performance criteria

Many-player games of optimal consumption and investment under relative performance criteria

Optimal Investment in a Large Population of Competitive and Heterogeneous Agents

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