Regulation, Volatility and Efficiency in Continuous-Time Markets
For researchers in market microstructure and power markets, this provides a theoretical trade-off between efficiency and volatility, but the results are theoretical without concrete numbers.
This paper models continuous-time markets with friction using stochastic differential equations and game theory, analyzing efficiency under optimal control and social cost functions. It presents an efficiency-volatility no-free-lunch trade-off theorem.
We analyze the efficiency of markets with friction, particularly power markets. We model the market as a dynamic system with $(d_t;\,t\geq 0)$ the demand process and $(s_t;\,t\geq 0)$ the supply process. Using stochastic differential equations to model the dynamics with friction, we investigate the efficiency of the market under an integrated expected undiscounted cost function solving the optimal control problem. Then, we extend the setup to a game theoretic model where multiple suppliers and consumers interact continuously by setting prices in a dynamic market with friction. We investigate the equilibrium, and analyze the efficiency of the market under an integrated expected social cost function. We provide an intriguing efficiency-volatility no-free-lunch trade-off theorem.