Optimal stopping in Uniswap v3 concentrated liquidity

Establish whether the optimal investment strategy for Uniswap v3 concentrated liquidity positions includes finite stopping times (i.e., an optimal decision to withdraw at a finite time).

Background

The authors analyze CPMM liquidity tokens as perpetual, fee-earning derivative positions and solve the associated risk-neutral valuation with optimal execution under their model.

They conjecture that in the concentrated liquidity framework of Uniswap v3—where liquidity is provided over a price range—the optimal strategy may require stopping at a finite time, implying a different and potentially more complex optimal stopping structure than in CPMMs.

References

In particular, we wish to highlight the concentrated liquidity designs of Uniswap v3; we conjecture that the optimal investment strategy for the concentrated liquidity would include finite stopping times which may complicate the risk-neutral pricing.

— DeFi Arbitrage in Hedged Liquidity Tokens (2409.11339 - Bichuch et al., 17 Sep 2024) in Section 6 (Conclusion)