A Mean-Field Conventional Asset Penalizing Game: A Study of Green Premium

This article presents a conventional asset penalizing game model in green finance. We use a Mean Field Game (MFG) approach to investigate how a large population of small interacting conventional asset holders influences green asset prices, resulting in a green asset premium. Firstly, we formulate the green premium for green assets in a decentralized exchange pool setting. Using a virtual curve to model how collective behavior affects green asset prices, we analyze green premium cost implications for agents. Then, we develop our MFG model for the transition of green assets. To address the MFG problem, we use the Pontryagin maximum principle to find the fix-point solution in a deterministic conventional asset price setting. In the numerical experiment, we expand it to the stochastic price case and use Monte Carlo simulations to obtain the equilibrium collective asset transfer rate under certain market conditions. For empirical analysis, we examine the explanatory power of our model concerning the real market's green premium.