arXiv subjects

G. Yin

Publications and source records attributed to G. Yin.

14 recordsLinked to original sources

arXiv2022

Mean-variance portfolio selection with dynamic attention behavior in a hidden Markov model

In this paper, we study closed-loop equilibrium strategies for mean-variance portfolio selection problem in a hidden Markov model with dynamic attention behavior. In addition to the investment strategy, the investor's attention to news is introduced as a control of the accuracy of the news signal process. The objective is to find equilibrium strategies by numerically solving an extended HJB equation by using Markov chain approximation method. An iterative algorithm is constructed and its convergence is established. Numerical examples are also provided to illustrate the results.

math.OC↗

arXiv2021

Stochastic Lotka-Volterra Competitive Reaction-Diffusion Systems Perturbed by Space-Time White Noise: Modeling and Analysis

Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation enables spatial dependence of the species. In addition, the noise process is allowed to be space-time white noise. In this work, wellposedness, regularity of solutions, existence of density, and existence of an invariant measure for stochastic reaction-diffusion systems with non-Lipschitz and non-linear growth coefficients and multiplicative noise are considered. By combining the random field approach and infinite integration theory approach in SPDEs for mild solutions, analysis is carried out. Then this paper develops a Lotka-Volterra competitive system under general setting; longtime properties are studied with the help of newly developed tools in stochastic calculus.

math.PR↗

arXiv2019

Stochastic Partial Differential Equation Models for Spatially Dependent Predator-Prey Equations

Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more versatile. To incorporate more qualitative features of the ratio-dependent models, the Beddington-DeAngelis functional response is also used. To analyze the systems under consideration, first existence and uniqueness of solutions of the SPDEs are obtained using the notion of mild solution. Then sufficient conditions for permanence and extinction are derived.

math.DS↗

arXiv2015

Classification of Asymptotic Behavior in A Stochastic SIR Model

This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition, this paper develops ergodicity of the underlying system. It is proved that the transition probabilities converge in total variation norm to the invariant measure. Our result gives a precise characterization of the support of the invariant measure. Rates of convergence are also ascertained. It is shown that the rate is not too far from exponential in that the convergence speed is of the form of a polynomial of any degree.

math.PR↗

arXiv2014

A wide-band tunable phase shifter for radio-frequency reflectometry

Radio-frequency reflectometry of nanodevices requires careful separation of signal quadratures to distinguish dissipative and dispersive contributions to the device impedance. A tunable phase shifter for this purpose is described and characterized. The phase shifter, consisting of a varactor-loaded transmission line, has the necessary tuning range combined with acceptable insertion loss across a frequency band 100 MHz - 1 GHz spanning most radio-frequency experiments. Its operation is demonstrated by demodulating separately the signals due to resistance and capacitance changes in a model device.

physics.ins-det↗

arXiv2014

Stability of Numerical Methods for Jump Diffusions and Markovian Switching Jump Diffusions

This work focuses on stability analysis of numerical solutions to jump diffusions and jump diffusions with Markovian switching. Due to the use of Poisson processes, using asymptotic expansions as in the usual approach of treating diffusion processes does not work. Different from the existing treatments of Euler-Maurayama methods for solutions of stochastic differential equations, we use techniques from stochastic approximation. We analyze the almost sure exponential stability and exponential $p$-stability. The benchmark test model in numerical solutions, namely, one-dimensional linear scalar jump diffusion is examined first and easily verifiable conditions are presented. Then Markovian regime-switching jump diffusions are dealt with. Moreover, analysis on stability of numerical methods for linearizable and multi-dimensional jump diffusions is carried out.

math.OC↗

arXiv2014

A Mean-Variance Control Framework for Platoon Control Problems: Weak Convergence Results and Applications on Reduction of Complexity

This paper introduces a new approach of treating platoon systems using mean-variance control formulation. The underlying system is a controlled switching diffusion in which the random switching process is a continuous-time Markov chain. This switching process is used to represent random environment and other random factors that cannot be given by stochastic differential equations driven by a Brownian motion. The state space of the Markov chain is large in our setup, which renders practically infeasible a straightforward implementation of the mean-variance control strategy obtained in the literature. By partitioning the states of the Markov chain into sub-groups (or clusters) and then aggregating the states of each cluster as a super state, we are able to obtain a limit system of much reduced complexity. The justification of the limit system is rigorously supported by establishing certain weak convergence results.

math.OC↗

arXiv2014

Stability of Nonlinear Regime-switching Jump Diffusions

Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First asymptotic stability in the large is obtained. Then the study on exponential p-stability is carried out. Connection between almost surely exponential stability and exponential p-stability is exploited. Also presented are smooth-dependence on the initial data. Using the smooth-dependence, necessary conditions for exponential p-stability are derived. Then criteria for asymptotic stability in distribution are provided. A couple of examples are given to illustrate our results.

math.OC↗

arXiv2014

Near-Optimal Mean-Variance Controls under Two-time-scale Formulations and Applications

Although the mean-variance control was initially formulated for financial portfolio management problems in which one wants to maximize expected return and control the risk, our motivations also stem from highway vehicle platoon controls that aim to maximize highway utility while ensuring zero accident. This paper develops near-optimal mean-variance controls of switching diffusion systems. To reduce the computational complexity, with motivations from earlier work on singularly perturbed Markovian systems \cite{SethiZ94,Yin&Zhang,GZB}, we use a two-time-scale formulation to treat the underlying systems, which is represented by use of a small parameter. As the small parameter goes to 0, we obtain a limit problem. Using the limit problem as a guide, we construct controls for the original problem, and show that the control so constructed is nearly optimal.

math.OC↗

arXiv2012

Sign-Error Adaptive Filtering Algorithms for Markovian Parameters

Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are time-varying and their dynamics are modeled by a discrete-time Markov chain. A distinctive feature of the algorithms is the multi-time-scale framework for characterizing parameter varia- tions and algorithm updating speeds. This is realized by considering the stepsize of the estimation algorithms and a scaling parameter that defines the transition rates of the Markov jump process. Depending on the relative time scales of these two pro- cesses, suitably scaled sequences of the estimates are shown to converge to either an ordinary differential equation, or a set of ordinary differential equations modulated by random switching, or a stochastic differential equation, or stochastic differential equa- tions with random switching. Using weak convergence methods, convergence and rates of convergence of the algorithms are obtained for all these cases.

math.OC↗

arXiv2010

Utility Maximization of an Indivisible Market with Transaction Costs

This work takes up the challenges of utility maximization problem when the market is indivisible and the transaction costs are included. First there is a so-called solvency region given by the minimum margin requirement in the problem formulation. Then the associated utility maximization is formulated as an optimal switching problem. The diffusion turns out to be degenerate and the boundary of domain is an unbounded set. One no longer has the continuity of the value function without posing further conditions due to the degeneracy and the dependence of the random terminal time on the initial data. This paper provides sufficient conditions under which the continuity of the value function is obtained. The essence of our approach is to find a sequence of continuous functions locally uniformly converging to the desired value function. Thanks to continuity, the value function can be characterized by using the notion of viscosity solution of certain quasi-variational inequality.

q-fin.PM↗

arXiv2009

Polarization Induced Switching Effect in Graphene Nanoribbon Edge-Defect Junction

With nonequilibrium Green's function approach combined with density functional theory, we perform an ab initio calculation to investigate transport properties of graphene nanoribbon junctions self-consistently. Tight-binding approximation is applied to model the zigzag graphene nanoribbon (ZGNR) electrodes, and its validity is confirmed by comparison with GAUSSIAN03 PBC calculation of the same system. The origin of abnormal jump points usually appearing in the transmission spectrum is explained with the detailed tight-binding ZGNR band structure. Transport property of an edge defect ZGNR junction is investigated, and the tunable tunneling current can be sensitively controlled by transverse electric fields.

cond-mat.mes-hall↗

arXiv2006

Existence of Saddle Points in Discrete Markov Games and Its Application in Numerical Methods for Stochastic Differential Games

This work establishes sufficient conditions for existence of saddle points in discrete Markov games. The result reveals the relation between dynamic games and static games using dynamic programming equations. This result enables us to prove existence of saddle points of non-separable stochastic differential games of regime-switching diffusions under appropriate conditions.

math.OC↗

arXiv2006

An Epsilon-uniform Finite Element Method for Singularly Perturbed Boundary Value Problems

This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new finite element solution always intersect with original one at fixed point. Using this fact, an effective epsilon-uniform approximation out of boundary is proposed by adding one point only in the grid that contains boundary layer. The thickness of boundary layer is not necessary to be known from priori estimation. Numerical results are carried out and compared to Shishkin mesh for demonstration purpose.

math.NA↗