Regulation, Volatility and Efficiency in Continuous-Time Markets

TL;DR

This paper models continuous-time power markets with friction, analyzing their efficiency and volatility through stochastic differential equations and game theory, revealing a fundamental trade-off between efficiency and volatility.

Contribution

It introduces a dynamic stochastic model of markets with friction and extends it to a game-theoretic setting to analyze equilibrium and efficiency.

Findings

Identifies a trade-off between market efficiency and volatility.

Develops a stochastic differential equation framework for market dynamics.

Establishes a no-free-lunch theorem relating efficiency and volatility.

Abstract

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.