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This paper investigates a stochastic linear-quadratic (SLQ, for short) control problem regulated by a time-invariant Markov chain in infinite horizon. Under the $L^2$-stability framework, we study a class of linear backward stochastic differential equations (BSDE, for short) in infinite horizon and discuss the open-loop and closed-loop solvabilities of the SLQ problem. The open-loop solvability is characterized by the solvability of a system of coupled forward-backward stochastic differential equations (FBSDEs, for short) in infinite horizon and the convexity of the cost functional, and the closed-loop solvability is shown to be equivalent to the open-loop solvability, which in turn is equivalent to the existence of a static stabilizing solution to the associated constrained coupled algebra Riccati equations (CAREs, for short). Under the uniform convexity assumption, we obtain the unique solvability of associated CAREs and construct the corresponding closed-loop optimal strategy. Finally, we also solve a class of discounted SLQ problems and give two concrete examples to illustrate the results developed in the earlier sections.

This paper studies a discrete-time mean-variance model based on reinforcement learning. Compared with its continuous-time counterpart in \cite{zhou2020mv}, the discrete-time model makes more general assumptions about the asset's return distribution. Using entropy to measure the cost of exploration, we derive the optimal investment strategy, whose density function is also Gaussian type. Additionally, we design the corresponding reinforcement learning algorithm. Both simulation experiments and empirical analysis indicate that our discrete-time model exhibits better applicability when analyzing real-world data than the continuous-time model., Comment: arXiv admin note: text overlap with arXiv:1904.11392 by other authors

This paper considers a stochastic linear quadratic problem for discrete-time systems with multiplicative noises over an infinite horizon. To obtain the optimal solution, we propose an online iterative algorithm of reinforcement learning based on Bellman dynamic programming principle. The algorithm avoids the direct calculation of algebra Riccati equations. It merely takes advantage of state trajectories over a short interval instead of all iterations, significantly simplifying the calculation process. Under the stabilizable initial values, numerical examples shed light on our theoretical results.

Sui Lutris is the first smart-contract platform to sustainably achieve sub-second finality. It achieves this significant decrease by employing consensusless agreement not only for simple payments but for a large variety of transactions. Unlike prior work, Sui Lutris neither compromises expressiveness nor throughput and can run perpetually without restarts. Sui Lutris achieves this by safely integrating consensuless agreement with a high-throughput consensus protocol that is invoked out of the critical finality path but ensures that when a transaction is at risk of inconsistent concurrent accesses, its settlement is delayed until the total ordering is resolved. Building such a hybrid architecture is especially delicate during reconfiguration events, where the system needs to preserve the safety of the consensusless path without compromising the long-term liveness of potentially misconfigured clients. We thus develop a novel reconfiguration protocol, the first to provably show the safe and efficient reconfiguration of a consensusless blockchain. Sui Lutris is currently running in production and underpins the Sui smart-contract platform. Combined with the use of Objects instead of accounts it enables the safe execution of smart contracts that expose objects as a first-class resource. In our experiments Sui Lutris achieves latency lower than 0.5 seconds for throughput up to 5,000 certificates per second (150k ops/s with transaction blocks), compared to the state-of-the-art real-world consensus latencies of 3 seconds. Furthermore, it gracefully handles validators crash-recovery and does not suffer visible performance degradation during reconfiguration.

The purpose of this paper is to extend the BML method proposed in Wang et al. [21] to make it applicable to more general coupled nonlinear FBSDEs. Compared to traditional methods, the extended BML method retains the advantage of being able to solve high-dimensional problems. In addition, this paper provides a theoretical interpretation of the proposed method. Finally, the feasibility of the proposed method is validated through numerical experiments.

In this note, we study a class of indefinite stochastic McKean-Vlasov linear-quadratic (LQ in short) control problem under the control taking nonnegative values. In contrast to the conventional issue, both the classical dynamic programming principle (DPP in short) and the usual Riccati equation approach fail. We tackle these difficulties by extending the state space from $\mathbb{R}$ to probability measure space, afterward derive the the corresponding the infinite dimensional Hamilton--Jacobi--Bellman (HJB in short) equation. The optimal control and value function can be obtained basing on two functions constructed via two groups of novelty ordinary differential equations satisfying the HJB equation mentioned before. As an application, we revisit the mean-variance portfolio selection problems in continuous time under the constraint that short-selling of stocks is prohibited. The investment risk and the capital market line can be captured simultaneously.

In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential equation. For this, we introduce an associated zero-sum stochastic differential game, where the state process is described by a classical stochastic differential equation (SDE, for short) with jumps, and the cost functional of recursive type is defined by a new type of backward stochastic differential equation (BSDE, for short) with two Poisson random measures, whose wellposedness and a prior estimate as well as the comparison theorem are investigated for the first time. One of the Poisson random measures appearing in the SDE and the BSDE stems from the integral term of the HJBI equations; the other random measure in BSDE is introduced to link the coupling factor of the HJBI equations. We show through an extension of the dynamic programming principle that the lower value function of this game problem is the viscosity solution of the system of our coupled HJBI equations. The uniqueness of the viscosity solution is also obtained in a space of continuous functions satisfying certain growth condition. In addition, also the upper value function of the game is shown to be the solution of the associated system of coupled Issacs' type of integral-partial differential equations. As a byproduct, we obtain the existence of the value for the game problem under the well-known Isaacs' condition., Comment: 37 pages

This paper employs a policy iteration reinforcement learning (RL) method to study continuous-time linear-quadratic mean-field control problems in infinite horizon. The drift and diffusion terms in the dynamics involve the states, the controls, and their conditional expectations. We investigate the stabilizability and convergence of the RL algorithm using a Lyapunov Recursion. Instead of solving a pair of coupled Riccati equations, the RL technique focuses on strengthening an auxiliary function and the cost functional as the objective functions and updating the new policy to compute the optimal control via state trajectories. A numerical example sheds light on the established theoretical results., Comment: 8 pages, 3 figures