I am looking for a continuous time model, that builds a game among a continuum of agents who interact strategically and they have mean-variance utility function. In particular mean-variance utility functions are defined as
$$U[X]=\mathbb{E}[X]-\delta_i\mathbb{V}ar[X]$$
where $X\in \mathbb{L}^2\left(\Omega,\mathcal{F},\mathbb{P}\right)$ is the random payoff while $\delta_i$ denotes the agent's risk aversion coefficient.
A continuous time model where the Nash equilibrium is build in the dynamic programming setting or as a system of backward looking stochastic differential equations. Has anybody seen anything like this?