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Nan-jing Huang

Publications and source records attributed to Nan-jing Huang.

At least 37 records · Page 2Linked to original sources
arXiv2023

Finite-time and fixed-time consensus control of multi-agent systems driven by parabolic partial differential equations

This paper focuses on the study of the finite-time consensus (FTC) and fixed-time consensus (FXC) issues of multi-agent systems (MASs) driven by parabolic partial differential equations (PDEs). Compared with the study in the existing literature, the topic of FTC and FXC control is first embodied in MASs driven by parabolic PDEs. Based on the Lyapunov theorems, the FTC and FXC controllers are devised to ensure that the MASs converge to a stable state with external disturbance. Furthermore, we simplify the controllers to guarantee the FTC and FXC of MASs without external disturbance. Finally, two illustrative examples are given to verify the feasibility of controllers.

math.OC↗
arXiv2022

Stochastic differential variational inequalities with applications

In this paper, we introduce and study a stochastic differential variational inequality (SDVI) which consists of a stochastic differential equation and a stochastic variational inequality. We obtain the existence and uniqueness of the solutions for SDVI by using the iteration method and Gronwall's inequality. Moreover, we show the convergence of Euler scheme for solving SDVI under some mild conditions. Finally, we apply the obtained results to solve the electrical circuits with diodes and the collapse of the bridge problems in stochastic environment.

math.OC↗
arXiv2022

Robust equilibrium strategy for mean-variance-skewness portfolio selection problem

This paper considers a robust time-consistent mean-variance-skewness portfolio selection problem for an ambiguity-averse investor by taking into account wealth-dependent risk aversion and wealth-dependent skewness preference as well as model uncertainty. The robust equilibrium investment strategy and corresponding equilibrium value function are characterized for such a problem by employing an extended Hamilton-Jacobi-Bellman-Isaacs (HJBI) system via a game theoretic approach. Furthermore, the robust equilibrium investment strategy and corresponding equilibrium value function are obtained in semi-closed form for a special robust time-consistent mean-variance-skewness portfolio selection problem. Finally, some numerical experiments are provided to indicate several new findings concerned with the robust equilibrium investment strategy and the utility losses.

math.OC↗
arXiv2021

A new class of differential quasivariational inequalities with an application to a quasistatic viscoelastic frictional contact problem

The overarching goal of this paper is to introduce and investigate a new nonlinear system driven by a nonlinear differential equation, a history-dependent quasivariational inequality, and a parabolic variational inequality in Banach spaces. Such a system can be used to model quasistatic frictional contact problems for viscoelastic materials with long memory, damage and wear. By using the Banach fixed point theorem, we prove an existence and uniqueness theorem of solution for such a system under some mild conditions. As a novel application, we obtain a unique solvability of a quasistatic viscoelastic frictional contact problem with long memory, damage and wear.

math.OC↗
arXiv2021

A Linear-quadratic Mean-Field Stochastic Stackelberg Differential Game with Random Exit Time

In this paper, we investigate a new model of a linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which the leader is allowed to stop her strategy at a random time. Our overarching goal is to find the Stackelberg solution of the leader and followers for such a model. By employing the backward induction method, the state equation is divided into two-stage equations. Moreover, by using the maximum principle and the verification theorem, the Stackelberg solution is obtained for such a model.

math.OC↗
arXiv2021

On Ekeland's variational principle for interval-valued functions with applications

In this paper, we obtain a version of Ekeland's variational principle for interval-value functions by means of the Dancs-Hegedus-Medvegyev theorem [14]. We also derive two versions of Ekeland's variational principle involving the generalized Hukuhara Gateaux differentiability of interval-valued functions as well as a version of Ekeland's variational principle for interval-valued bifunctions. Finally, we apply these new versions of Ekeland's variational principle to fixed point theorems, to interval-valued optimization problems, to the interval-valued Mountain Pass Theorem, to noncooperative interval-valued games, and to interval-valued optimal control problems described by interval-valued differential equations.

math.OC↗
arXiv2021

Set-valued Ito's formula with an application to the general set-valued backward stochastic differential equation

The overarching goal of this paper is to establish a set-valued Itô's formula. As an application, we obtain the existence and uniqueness of solutions for the general set-valued backward stochastic differential equation which gives an answer to an open question proposed by Ararat et al. (C. Ararat, J. Ma and W.Q. Wu, Set-valued backward stochastic differential equation, arXiv:2007.15073).

math.PR↗
arXiv2020

A new class of fractional impulsive differential hemivariational inequalities with an application

We consider a new fractional impulsive differential hemivariational inequality which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework. By utilizing a surjectivity theorem and a fixed point theorem, we establish an existence and uniqueness theorem for such a problem. Moreover, we investigate the perturbation problem of the fractional impulsive differential hemivariational inequality to prove a convergence result which describes the stability of the solution in relation to perturbation data. Finally, our main results are applied to obtain some new results for a frictional contact problem with the surface traction driven by the fractional impulsive differential equation.

math.OC↗
arXiv2020

Global Mittag-Leffler stability of Fractional-Order Projection Neural Networks with Impulses

This paper is about the study of a new class of fractional-order projection neural networks with impulses which capture the desired features of both the variational inequality and the fractional-order impulsive dynamical systems within the same framework. We obtain the existence and boundedness of solutions for such fractional-order projection neural networks under mild conditions. Moreover, we give some sufficient conditions for ensuring the global Mittag-Leffler stability of the equilibrium point for such fractional-order projection neural networks by utilizing a general quadratic Lyapunov function. Finally, we provide two numerical examples to illustrate the validity and feasibility of the main results.

math.OC↗
arXiv2020

Globalized distributionally robust optimization problems under the moment-based framework

This paper is devoted to reduce the conservatism of distributionally robust optimization with moments information. Since the optimal solution of distributionally robust optimization is required to be feasible for all uncertain distributions in a given ambiguity distribution set and so the conservatism of the optimal solution is inevitable. To address this issue, we introduce the globalized distributionally robust counterpart (GDRC) which allows constraint violations controlled by functional distance of the true distribution to the inner uncertainty distribution set. We obtain the deterministic equivalent forms for several GDRCs under the moment-based framework. To be specific, we show the deterministic equivalent system of inequalities for the GDRCs under second order moment information with a separable distance function and a jointly convex distance function, respectively. Moreover, the feasible set of the system is convex. We also develop the deterministic equivalent inequality for the GDRC under first order moment and support information. The computationally tractable examples are presented for these GDRCs. A numerical tests of a portfolio optimization problem is given to show the efficiency of our methods and the results demonstrate that the globalized distributionally robust solutions is non-conservative and flexible compared to the distributionally robust solutions.

math.OC↗
arXiv2020

A stochastic optimal control problem governed by SPDEs via a spatial-temporal interaction operator

In this paper, we first introduce a new spatial-temporal interaction operator to describe the space-time dependent phenomena. Then we consider the stochastic optimal control of a new system governed by a stochastic partial differential equation with the spatial-temporal interaction operator. To solve such a stochastic optimal control problem, we derive an adjoint backward stochastic partial differential equation with spatial-temporal dependence by defining a Hamiltonian functional, and give both the sufficient and necessary (Pontryagin-Bismut-Bensoussan type) maximum principles. Moreover, the existence and uniqueness of solutions are proved for the corresponding adjoint backward stochastic partial differential equations. Finally, our results are applied to study the population growth problems with the space-time dependent phenomena.

math.OC↗
arXiv2019

Variational and numerical analysis of a dynamic viscoelastic contact problem with friction and wear

In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational inequality by employing the variational method. We adopt the Rothe method to show the existence and uniqueness of weak solution for the hyperbolic quasi-variational inequality under mild conditions. We also give a fully discrete scheme for solving the hyperbolic quasi-variational inequality and obtain error estimates for the fully discrete scheme.

math.OC↗
arXiv2019

Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memory

In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy, price impact and price volatility are obtained explicitly. The volatility of the price volatility appears excessive, which is a result of the fact that a more aggressive trading strategy is chosen by the insider when uninformed volume is higher. The optimal trading strategy turns out to possess the property of long memory, and the price impact is also affected by the fractional noise.

q-fin.MF↗
arXiv2018

Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity

In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous model. Moreover, discrete and continuous sampled volatility swap pricing formulas are given by employing transform techniques and the relationship between two pricing formulas is discussed. Finally, some numerical simulations are reported to support the results presented in this paper.

q-fin.PR↗
arXiv2018

Variance swaps under Lévy process with stochastic volatility and stochastic interest rate in incomplete markets

This paper focuses on the pricing of the variance swap in an incomplete market where the stochastic interest rate and the price of the stock are respectively driven by Cox-Ingersoll-Ross model and Heston model with simultaneous Lévy jumps. By using the equilibrium framework, we obtain the pricing kernel and the equivalent martingale measure. Moreover, under the forward measure instead of the risk neural measure, we give the closed-form solution for the fair delivery price of the discretely sampled variance swap by employing the joint moment generating function of the underlying processes. Finally, we provide some numerical examples to depict that the values of variance swaps not only depend on the stochastic interest rates but also increase in the presence of jump risks.

q-fin.PR↗
arXiv2017

Fractional Wishart Processes and $\varepsilon$-Fractional Wishart Processes with Applications

In this paper, we introduce two new matrix stochastic processes: fractional Wishart processes and $\varepsilon$-fractional Wishart processes with integer indices which are based on the fractional Brownian motions and then extend $\varepsilon$-fractional Wishart processes to the case with non-integer indices. Both of two kinds of processes include classic Wishart processes when the Hurst index $H$ equals $\frac{1}{2}$ and present serial correlation of stochastic processes. Applying $\varepsilon$-fractional Wishart processes to financial volatility theory, the financial models account for the stochastic volatilities of the assets and for the stochastic correlations not only between the underlying assets' returns but also between their volatilities and for stochastic serial correlation of the relevant assets.

math.OC↗