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ABSTRACT This paper is concerned with the problem of capital provision in a large particle system modeled by stochastic differential equations involving hitting times, which arises from considerations of systemic risk in a financial network. Motivated by Tang and Tsai, we focus on the number or proportion of surviving entities that never default to measure the systemic robustness. First we show that the mean‐field particle system and its limit McKean–Vlasov equation are both well‐posed by virtue of the notion of minimal solutions. We then establish a connection between the proportion of surviving entities in the large particle system and the probability of default in the McKean–Vlasov equation as the size of the interacting particle system tends to infinity. Finally, we study the asymptotic efficiency of capital provision for different drift , which is linked to the economy regime: The expected number of surviving entities has a uniform upper bound if ; it is of order if ; and it is of order if , where the effect of capital provision is negligible. 

Abstract We develop a continuous‐time control approach to optimal trading in a Proof‐of‐Stake (PoS) blockchain, formulated as a consumption‐investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton–Jacobi–Bellman (HJB) equations. When the utility functions are linear or convex, we derive close‐form solutions and show that the bang‐bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk‐adjusted valuation of the stakes. In particular, we show when a participant is risk‐neutral or risk‐seeking, corresponding to the risk‐adjusted valuation being a martingale or a sub‐martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk‐control version of the consumption‐investment problem; and for a special case, the “stake‐parity” problem, we show a mean‐reverting strategy is optimal. 

Preference tuning is a crucial process for aligning deep generative models with human preferences. This survey offers a thorough overview of recent advancements in preference tuning and the integration of human feedback. The paper is organized into three main sections: 1) introduction and preliminaries: an introduction to reinforcement learning frameworks, preference tuning tasks, models, and datasets across various modalities: language, speech, and vision, as well as different policy approaches, 2) in-depth exploration of each preference tuning approach: a detailed analysis of the methods used in preference tuning, and 3) applications, discussion, and future directions: an exploration of the applications of preference tuning in downstream tasks, including evaluation methods for different modalities, and an outlook on future research directions. Our objective is to present the latest methodologies in preference tuning and model alignment, enhancing the understanding of this field for researchers and practitioners. We hope to encourage further engagement and innovation in this area. Additionally, we provide a GitHub link https://github.com/hanyang1999/Preference-Tuning-with-Human-Feedback.