Study Majorana Neutrino Contribution to B-meson Semi-leptonic Rare Decays

B meson semi-leptonic rare decays are sensitive to new physics beyond standard model. We study the $B^{-}\to \pi^{-}\mu^{+}\mu^{-}$ process and investigate the Majorana neutrino contribution to its decay width. The constraints on the Majorana neutrino mass and mixing parameter are obtained from this decay channel with the latest LHCb data. Utilizing the best fit for the parameters, we study the lepton number violating decay $B^{-}\to \pi^{+}\mu^{-}\mu^{-}$, and find its branching ratio is about $6.4\times10^{-10}$, which is consistent with the LHCb data reported recently.Comment: 10 pages, 3 figure

Comparison theorems for multi-dimensional BSDEs with jumps and applications to constrained stochastic linear-quadratic control

In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for one-dimensional case. Using these and other delicate tools, we then construct solutions to coupled two-dimensional stochastic Riccati equation with jumps in both standard and singular cases. In the end, these results are applied to solve a cone-constrained stochastic linear-quadratic and a mean-variance portfolio selection problem with jumps. Different from no jump problems, the optimal (relative) state processes may change their signs, which is of course due to the presence of jumps

Constrained stochastic LQ control with regime switching and application to portfolio selection

This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients, and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and the Markov chain. Using It\^{o}'s lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ESREs). We prove the existence and uniqueness of the two ESREs using tools including multidimensional comparison theorem, truncation function technique, log transformation and the John-Nirenberg inequality. These results are then applied to study mean-variance portfolio selection problems with and without short-selling prohibition with random parameters depending on both the Brownian motion and the Markov chain. Finally, the efficient portfolios and efficient frontiers are presented in closed forms

Constrained monotone mean-variance problem with random coefficients

This paper studies the monotone mean-variance (MMV) problem and the classical mean-variance (MV) problem with convex cone trading constraints in a market with random coefficients. We provide semiclosed optimal strategies and optimal values for both problems via certain backward stochastic differential equations (BSDEs). After noting the links between these BSDEs, we find that the two problems share the same optimal portfolio and optimal value. This generalizes the result of Shen and Zou $[$ SIAM J. Financial Math., 13 (2022), pp. SC99-SC112$]$ from deterministic coefficients to random ones

Robust output regulation of linear system subject to modeled and unmodeled uncertainty

In this paper, a novel robust output regulation control framework is proposed for the system subject to noise, modeled disturbance and unmodeled disturbance to seek tracking performance and robustness simultaneously. The output regulation scheme is utilized in the framework to track the reference in the presence of modeled disturbance, and the effect of unmodeled disturbance is reduced by an $\mathcal{H}_\infty$ compensator. The Kalman filter can be also introduced in the stabilization loop to deal with the white noise. Furthermore, the tracking error in the presence/absence of noise and disturbance is estimated. The effectiveness and performance of our proposed control framework is verified in the numerical example by applying in the Furuta Inverted Pendulum system

No-Regret Learning in Dynamic Competition with Reference Effects Under Logit Demand

This work is dedicated to the algorithm design in a competitive framework, with the primary goal of learning a stable equilibrium. We consider the dynamic price competition between two firms operating within an opaque marketplace, where each firm lacks information about its competitor. The demand follows the multinomial logit (MNL) choice model, which depends on the consumers' observed price and their reference price, and consecutive periods in the repeated games are connected by reference price updates. We use the notion of stationary Nash equilibrium (SNE), defined as the fixed point of the equilibrium pricing policy for the single-period game, to simultaneously capture the long-run market equilibrium and stability. We propose the online projected gradient ascent algorithm (OPGA), where the firms adjust prices using the first-order derivatives of their log-revenues that can be obtained from the market feedback mechanism. Despite the absence of typical properties required for the convergence of online games, such as strong monotonicity and variational stability, we demonstrate that under diminishing step-sizes, the price and reference price paths generated by OPGA converge to the unique SNE, thereby achieving the no-regret learning and a stable market. Moreover, with appropriate step-sizes, we prove that this convergence exhibits a rate of $\mathcal{O}(1/t)$