  An automated market maker (AMM) is a state machine that manages pools of
assets, allowing parties to buy and sell those assets according to a fixed
mathematical formula. AMMs are typically implemented as smart contracts on
blockchains, and its prices are kept in line with the overall market price by
arbitrage: if the AMM undervalues an asset with respect to the market, an
"arbitrageur" can make a risk-free profit by buying just enough of that asset
to bring the AMM's price back in line with the market.
  AMMs, however, are not designed for assets that expire: that is, assets that
cannot be produced or resold after a specified date. As assets approach
expiration, arbitrage may not be able to reconcile supply and demand, and the
liquidity providers that funded the AMM may have excessive exposure to risk due
to rapid price variations.
  This paper formally describes the design of a decentralized exchange (DEX)
for assets that expire, combining aspects of AMMs and limit-order books. We
ensure liveness and market clearance, providing mechanisms for liquidity
providers to control their exposure to risk and adjust prices dynamically in
response to situations where arbitrage may fail.
