Related papers: G3M Impermanent Loss Dynamics
Motivated by various distributed control applications, we consider a linear system with Gaussian noise observed by multiple sensors which transmit measurements over a dynamic lossy network. We characterize the stationary optimal sensor…
We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded…
A currency with stable purchasing power can always provide a psychological haven for people around the world. However, since the collapse of the Bretton Woods system, issuing more cheap currencies has become a common trend in the…
This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail,…
Recent advances in imitation learning for 3D robotic manipulation have shown promising results with diffusion-based policies. However, achieving human-level dexterity requires seamless integration of geometric precision and semantic…
Constant Function Market Makers (CFMMs) are a tool for creating exchange markets, have been deployed effectively in prediction markets, and are now especially prominent in the Decentralized Finance ecosystem. We show that for any set of…
We introduce simplicial persistence, a measure of time evolution of network motifs in subsequent temporal layers. We observe long memory in the evolution of structures from correlation filtering, with a two regime power law decay in the…
We provide several algorithms for constrained optimization of a large class of convex problems, including softmax, $\ell_p$ regression, and logistic regression. Central to our approach is the notion of width reduction, a technique which has…
We introduce a geometric theory of payment channel networks that centers the polytope $W_G$ of feasible wealth distributions; liquidity states $L_G$ project onto $W_G$ via strict circulations. A payment is feasible iff the post-transfer…
The Geometric Brownian Motion (GBM) is a standard model in quantitative finance, but the potential function of its stochastic differential equation (SDE) cannot include stable nonzero prices. This article generalises the GBM to an SDE with…
We consider an expected utility maximization problem where the utility function is not necessarily concave and the time horizon is uncertain. We establish a necessary and sufficient condition for the optimality for general non-concave…
Conditional depth execution routes a subset of tokens through a lightweight cheap FFN while the remainder execute the standard full FFN at each controlled layer. The central difficulty is gate training: the gate decision must propagate…
Although modern blockchains almost universally produce blocks at fixed intervals, existing models still lack an analytical formula for the loss-versus-rebalancing (LVR) incurred by Automated Market Makers (AMMs) liquidity providers in this…
Regardless of the selected asset class and the level of model complexity (Transformer versus LSTM versus Perceptron/RNN), the GMADL loss function produces superior results than standard MSE-type loss functions and has better numerical…
Decentralized exchanges (DEXes) have evolved dramatically since the introduction of Automated Market Makers (AMMs). In recent years, solver-based protocols have emerged as an alternative venue aiming to introduce competition for routing,…
Automated Market Makers face a geometric dilemma: expanding liquidity depth to reduce execution slippage increases Liquidity Providers' exposure to toxic arbitrage, quantified as Loss-Versus-Rebalancing (LVR). We study the Hybrid…
Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which…
Recently, 3D vision-based diffusion policies have shown strong capability in learning complex robotic manipulation skills. However, a common architectural mismatch exists in these models: a tiny yet efficient point-cloud encoder is often…
The ability to learn multi-modal action distributions is indispensable for robotic manipulation policies to perform precise and robust control. Flow-based generative models have recently emerged as a promising solution to learning…
This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good…