SREC markets are a market-based system designed to incentivize solar energy generation. A regulatory body imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a certificate for each MWh generated. Regulated firms seek to navigate the market to minimize the cost imposed on them, by modulating their SREC generation and trading activities. As such, the SREC market can be viewed through the lens of a large stochastic game with heterogeneous agents, where agents interact through the market price of the certificates. We study this stochastic game by solving the mean-field game (MFG) limit with sub-populations of heterogeneous agents. Our market participants optimize costs accounting for trading frictions, cost of generation, SREC penalty, and generation uncertainty. Using techniques from variational analysis, we characterize firms' optimal controls as the solution of a new class of McKean-Vlasov FBSDE and determine the equilibrium SREC price. We further prove that MFG strategy has the -Nash property for the finite player game. Finally, we numerically solve the MV-FBSDEs and conclude by demonstrating how firms behave in equilibrium using simulated examples.

SREC markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar power in a given period and provides them with certificates for each generated MWh. Firms offset these certificates against the floor and pay a penalty for any lacking certificates. Certificates are tradable assets, allowing firms to purchase/sell them freely. In this work, we formulate a stochastic control problem for generating and trading in SREC markets from a regulated firm's perspective. We account for generation and trading costs, the impact both have on SREC prices, provide a characterization of the optimal strategy, and develop a numerical algorithm to solve this control problem. Through numerical experiments, we explore how a firm who acts optimally behaves under various conditions. We find that an optimal firm's generation and trading behaviour can be separated into various regimes, based on the marginal benefit of obtaining an additional SREC, and validate our theoretical characterization of the optimal strategy. We also conduct parameter sensitivity experiments.

We found a significant number of missing, erroneous, and outlying vital signs measurements in a large ICU database. Our results provide empirical evidence of the nonrepresentativeness of hourly vital signs. Additional studies should focus on determining optimal sampling frequencies for recording vital signs in the ICU.

Solar renewable energy certificate (SREC) markets are a market-based system that incentivizes solar energy generation. A regulatory body overseeing load serving entities imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a tradeable certificate for each MWh generated. Firms seek to navigate the market optimally by modulating their SREC generation and trading rates.As such, the SREC market can be viewed as a stochastic game, where agents interact through the SREC price.We study this stochastic game by solving the meanfield game (MFG) limit with subpopulations of heterogeneous agents. Market participants optimize costs accounting for trading frictions, cost of generation, nonlinear noncompliance costs, and generation uncertainty.Moreover, we endogenize SREC price through market clearing. We characterize firms' optimal controls as the solution of McKean-Vlasov (MV) forward-backward stochastic differential equations (FBSDEs) and determine the equilibrium SREC price. We establish the existence and uniqueness of a solution to this MV-FBSDE, and prove that the MFG strategies form an 𝜖-Nash equilibrium for the finite player game. Finally, we develop a numerical scheme for solving the MV-FBSDEs and conduct a simulation study.

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