I have been reading this paper by Yang Liu, Lukas Schmid and Amir Yaron, which contains a very elegant mechanism that generates an endogenous liquidity premium for US government debt. However, I got confused by something.

In that paper, households have liquidity needs that arrive with probability $\lambda_t$ with magnitude $\xi_t$. To meet these liquidity needs, they need to sell off some of their assets. In so doing, they incur a cost $\nu_t$. This cost then enters the budget constraint (page 9, first equation). But from the first equation on page 11, it is clear this cost is an average (averaged across shock magnitudes $\xi_t \sim \Phi_\xi$).

The households are not risk-neutral, so they should care about the variance of the costs, but implicitly the authors seem to be imposing that they don't. I emailed the authors about this, but never received a response. I would be very grateful if someone could point out what I am missing. Thanks in advance!



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