Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. Arbitrage trades have been shown to align the prices reported by CFMMs with those external markets. These impose costs Liquidity Providers (LPs) who supply reserves CFMMs. Trading fees proposed as mechanism for compensating LPs arbitrage ...

We show the existence of Lipschitz-in-space optimal controls for a class mean-field control problems with dynamics given by non-local continuity equation. The proof relies on vanishing viscosity method: we prove convergence same problem where diffusion term is added, small parameter. By using stochastic control, first sequence diffusion. then build optimizer original letting parameter go to zero.

achieving optimal production cycle time for improving manufacturing processes is one of the common problems in production planning. during recent years, different approaches have been developed for solving this problem, but most of them assume that mean quality characteristic is constant over production run length and sets it on customer’s target value. however, the process mean may drift from ...

In this paper, we present the best possible upper and lower bounds for the Sándor-Yang mean in terms of the power mean. Mathematics subject classification (2010): 26E60.

Recent studies have shown that the variable sampling interval (VSI) scheme helps practitioners detect process shifts more quickly than the classical scheme (FRS). In this paper, the economically and statistically optimal design of the VSI T2 control chart for monitoring the process mean vector is investigated. The cost model proposed by Lorenzen and Vance (1986) is minimized through a genetic a...