Applications of Mean Field Theory in Management Science
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The main objective of my PhD study is to understand an aggregate effect arising from a large number of agents who have a similar aspect of decision markings and objectives. The primary idea of mean field approach is that the individual agent makes a decision by considering the distribution of the other agents rather than assuming that all agents’ detailed information on states is collectible. In the first essay of my dissertation, the primary objective is to study the optimal consumption and portfolio selection problem of risk-controlled investors who strive to maximize their utility of both consumption and terminal wealth. Risk is measured by the variance of terminal wealth, which introduces a nonlinear function of the expected value into the control problem, so a standard stochastic control theory is not properly applicable. This control problem is totally open until the discovery of mean field type control. The second essay explores the dynamic competition among a large number of interacting households who own local storage with a self-generated renewable energy system, and each can decide the amount of charging or discharging energy based on the market environment and the level of energy stored. Under the mean field setting, the optimal solution can be interpreted as an optimal policy suggestion by a central planner who is willing to increase the penetration of local storage to enhance the resilience of the grid system. The third essay investigates a new control problem for dealer’s optimal markup and inventory control regarding Over-The-Counter (OTC) trades. The explicit solutions obtained by the mean field approach can contribute to developing a decision support system for dealers willing to coordinate an inter-dealer and investor-dealer market simultaneously. The proposed decision-making rules may facilitate dealers’ responses to imbalances in demand and supply to reduce the possibility of policy intervention about liquidity risk in OTC markets.