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Abstract In this paper, we show how relaxation techniques can be used to establish the existence of an optimal contract in the presence of information asymmetry. The method we illustrate was initially motivated by the problem of designing optimal brokerage fees, but it does apply to other optimal contract problems in which (i) the agent controls linearly the drift of a diffusion process, (ii) the direct dependence of the principal’s and the agent’s objectives on the strategy of the agent is of a special form, and (iii) the space of admissible contracts is compact. This method is then applied to establish the existence of an optimal brokerage fee in a market model with a private trading signal observed by the broker’s client, but not by the broker.
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Automated Market Making and Arbitrage Profits in the Presence of Fees
We consider the impact of trading fees on the profits of arbitrageurs trading against an automated marker marker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to both introduce fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of time that an arriving arbitrageur finds a profitable trade.
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- Award ID(s):
- 2212745
- PAR ID:
- 10511530
- Publisher / Repository:
- Financial Cryptography
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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