represents the instantaneous rate of consumption of agent $i$, so that $c^i_t$ is the rate per unit wealth. We say that a portfolio strategy is admissible if it belongs to the set $\A$ of $\FF$-progressively measurable $\R \times \R_+$-valued process $(\pi_t, c_t)_{t \in [0,T]}$ satisfying $\E  \int_0^T (\pi_t^2 + c_t^2)dt < \infty$. Throughout the paper, $\R_+ :=(0,\infty)$ denotes the *strictly* positive reals, and we do not allow a consumption rate of zero. This is reasonable and less restrictive than it may at first appear because the form of our utility functions, introduced in the next paragraph, will ensure that agents’ marginal utilities approach $+\infty$ as consumption approaches zero. Note also that for any admissible portfolio strategy we have $X^i_t > 0$ for all $t \in [0,T]$. Indeed, we parametrized our consumption process as we did in in part to avoid the possibility of bankruptcy and in part to avoid imposing any state constraints.

The utility function of each agent belongs to the family of power (CRRA) utilities, $$U(x; \delta) = \begin{cases}
        \frac{1}{1 - 1 / \delta}x^{1 - 1 / \delta} & \text{ if } \delta \ne 1 \\
        \log x & \text{ if } \delta = 1,
    \end{cases}$$ defined for 