Trading in CEXs and DEXs with Priority Fees and Stochastic Delays

TL;DR

The paper develops a mixed-control framework where a continuous trading rate on a CEX is combined with impulse submissions to a DEX under stochastic execution delays whose mean can be controlled. It proves a dynamic programming principle and shows that the value function solves a Hamilton–Jacobi–Bellman quasi-variational inequality in the viscosity sense, with a nonlocal impulse operator capturing asynchronous executions. Applied to a CEX-DEX arbitrage problem, it derives optimal priority-fee policies that depend on time, inventory, and price dislocations, and demonstrates substantial outperformance over non-strategic fee choices, with diminishing gains as the fee set grows. The work advances both the mathematical treatment of latency in optimal execution and practical latency-risk management in decentralized finance.

Abstract

We develop a mixed control framework that combines absolutely continuous controls with impulse interventions subject to stochastic execution delays. The model extends current impulse control formulations by allowing (i) the controller to choose the mean of the stochastic delay of their impulses, and allowing (ii) for multiple pending orders, so that several impulses can be submitted and executed asynchronously at random times. The framework is motivated by an optimal trading problem between centralized (CEX) and decentralized (DEX) exchanges. In DEXs, traders control the distribution of the execution delay through the priority fee paid, introducing a fundamental trade-off between delays, uncertainty, and costs. We study the optimal trading problem of a trader exploiting trading signals in CEXs and DEXs. From a mathematical perspective, we derive the associated dynamic programming principle of this new class of impulse control problems, and establish the viscosity properties of the corresponding quasi-variational inequalities. From a financial perspective, our model provides insights on how to carry out execution across CEXs and DEXs, highlighting how traders manage latency risk optimally through priority fee selection. We show that employing the optimal priority fee has a significant outperformance over non-strategic fee selection.

Figures (6)

• Figure 1: Value function and exercise region as a function of the CEX and DEX prices $(s,z)$ for $q=0$.
• Figure 2: Optimal trading rate $\nu^*$ as a function of the CEX price $s$ and the inventory $q$ for $z=2700$ and $t=0.1$.
• Figure 3: Exercise and continuation regions as a function of the CEX and DEX prices $(s,z)$ at time indices $t_0<t_1<t_2$ for $q=40$. Here, $t_0=0.2$, $t_1=0.5$, and $t_2 = 0.8$.
• Figure 4: Priority fees as a function of the CEX and DEX prices $(s,z)$ at time indices $t_0<t_1<t_2$ for $q=0$. Here, $t_0=0.2$, $t_1=0.5$, and $t_2 = 0.8$.
• Figure 5: Priority fee regions for increasing exogenous arrival intensities at the CEX and DEX at time $t = 0.5$. From left to right, all arrival intensities are jointly increased $\mathfrak{l}_2<\mathfrak{l}_1<\mathfrak{l}_0$.

Theorems & Definitions (31)

• Lemma 2.1
• proof
• Proposition 2.2
• proof
• Lemma 2.3: Quadratic growth
• proof
• Theorem 3.1: Dynamic Programming Principle
• proof
• Remark 3.2
• Definition 3.3: Viscosity solution