arXiv subjects

Jiongmin Yong

Publications and source records attributed to Jiongmin Yong.

At least 19 recordsLinked to original sources

arXiv2026

Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional in Infinite Horizon

This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional in an infinite horizon. A main difficult is well-posedness of the BSDE in $L^1$ and in infinite horizon. A notion of weighted $L^2$-stabilizability is introduced and characterized, which will lead to an equivalence of the optimal control problem having recursive cost functional with a classical LQ problem. Then all the results of classical problems for open-loop and closed-loop solvability of such an LQ problem can be translated, in terms of the solvability of a forward-backward stochastic differential equation and that of algebraic Riccati equation. Finally, the nonhomogeneous is discussed.

math.OC↗

arXiv2026

Long-Time Behaviors of Stochastic Linear-Quadratic Optimal Control Problems

This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of the well-known cell problem in the homogenization of Hamilton-Jacobi equations. By establishing a connection between this problem and the ergodic cost problem, we reveal the turnpike properties of the linear-quadratic stochastic optimal control problems from various perspectives.

math.OC↗

arXiv2026

Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional

This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional. It involves BSDEs in $L^1$ whose well-posedness is a subtle issue. A suitable framework has been adopted so that the corresponding LQ problem is correctly formulated. Open-loop and closed-loop solvability of such an LQ problem have been investigated and characterized by the solvability of an FBSDE and that of Riccati differential equation.

math.OC↗

arXiv2025

Stochastic Optimal Impulse Controls with Changing Running Costs

This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle is to be used. The corresponding Hamilton-Jacobi-Bellman (HJB) equation (a quasi-variational inequality) is derived, which contains a parameter. The value function is a unique viscosity solution to this HJB equation by a classical argument. Further, inspired by the derivation of the Pontryagin type maximum principle for stochastic optimal controls with a non-convex control domain, we have established the maximum principle for our stochastic optimal impulse controls, allowing perturbations in optimal impulse moments.

math.OC↗

arXiv2025

A Time-Inconsistent Stochastic Optimal Control Problem in an Infinite Time Horizon

This paper is concerned with a time-inconsistent stochastic optimal control problem in an infinite time horizon with a non-degenerate diffusion in the state equation. A major assumption is that people become rational after a large time. Under such a condition, the problem in an infinite time horizon can be decomposed into two parts: a non-autonomous time-consistent problem in an infinite time horizon and a time-inconsistent problem in a finite time horizon. Then an equilibrium strategy will be constructed. Both Bolza type problem and recursive cost problem are considered.

math.OC↗

arXiv2025

Turnpike Property of a Linear-Quadratic Optimal Control Problem in Large Horizons with Regime Switching II: Non-Homogeneous Cases

This paper is concerned with an optimal control problem for a nonhomogeneous linear stochastic differential equation having regime switching with a quadratic functional in the large time horizon. This is a continuation of the paper \cite{Mei-Wang-Yong-2025}, in which the strong turnpike property was established for homogeneous linear systems with purely quadratic cost functionals. We extend the results to the current situation. It turns out that some of the results are new even for the cases without regime switchings.

math.OC↗

arXiv2025

Mean-Field Stochastic Linear-Quadratic Optimal Controls: Roles of Expectation and Conditional Expectation Operators

This paper investigates a mean-field linear-quadratic optimal control problem where the state dynamics and cost functional incorporate both expectation and conditional expectation terms. We explicitly derive the pre-committed, na\"ıve, and equilibrium solutions and establish the well-posedness of the associated Riccati equations. This reveals how the expectation and conditional expectation operators influence time-consistency.

math.OC↗

arXiv2025

Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases

This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike properties for the optimal pairs. The key is to prove a proper convergence of the solutions to the differential Riccati equations to the algebraic Riccati equation. Even for the problems without regime switchings, our result provides a refined estimate compared to those in the previous literature, which also provides a new tool for further research.

math.OC↗

arXiv2025

Infinite Horizon Mean-Field Linear-Quadratic Optimal Control Problems with Switching and Indefinite-Weighted Costs

This paper is concerned with an infinite horizon stochastic linear quadratic (LQ, for short) optimal control problems with conditional mean-field terms in a switching environment. Different from [17], the cost functionals do not have positive-definite weights here. When the problems are merely finite, we construct a sequence of asymptotic optimal controls and derive their closed-loop representations. For the solvability, an equivalence result between the open-loop and closed-loop cases is established through algebraic Riccati equations and infinite horizon backward stochastic differential equations. It can be seen that the research in [17] with positive-definite weights is a special case of the current paper.

math.OC↗

arXiv2025

Linear-Quadratic Optimal Control for Mean-Field Stochastic Differential Equations in Infinite-Horizon with Regime Switching

This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with conditional mean-field term in a switching regime environment. The orthogonal decomposition introduced in [21] has been adopted. Desired algebraic Riccati equations (AREs, for short) and a system of backward stochastic differential equations (BSDEs, for short) in infinite time horizon with the coefficients depending on the Markov chain have been derived. The determination of closed-loop optimal strategy follows from the solvability of ARE and BSDE. Moreover, the solvability of BSDEs leads to a characterization of open-loop solvability of the optimal control problem.

math.OC↗

arXiv2024

A Limit Order Book Model for High Frequency Trading with Rough Volatility

We introduce a model for limit order book of a certain security with two main features: First, both the limit orders and market orders for the given asset are allowed to appear and interact with each other. Second, the high frequency trading activities are allowed and described by the scaling limit of nearly-unstable multi-dimensional Hawkes processes with power law decay. The model has been derived as a stochastic partial differential equation (SPDE, for short), under certain intuitive identifications. Its diffusion coefficient is determined by a Volterra integral equation driven by a Hawkes process, whose Hurst exponent is less than 1/2 (so that the relevant process is negatively correlated). As a result, the volatility path of the SPDE is rougher than that driven by a (standard) Brownian motion. The well-posedness follows from a result in literature. Hence, a foundation is laid down for further studies in this direction.

q-fin.PR↗

arXiv2024

Solvability of Coupled Forward-Backward Volterra Integral Equations

Motivated by the optimality system associated with controlled (forward) Volterra integral equations (FVIEs, for short), the well-posedness of coupled forward-backward Voterra integral equations (FBVIEs, for short) is studied. The main feature of FBVIEs is that the unknown $\{(X(t,s),Y(t,s))\}$ has two arguments. By taking $t$ as a parameter and $s$ as a (time) variable, one can regard FBVIE as a system of ordinary differential equations (ODEs, for short), with infinite-dimensional space values $\{(X(\cdot,s),Y(\cdot,s));\,s\in[0,T]\}$. To establish the well-posedness of such an FBVIE, a new non-local monotonicity condition is introduced, by which a bridge in infinite-dimensional spaces is constructed. Then by generalizing the method of continuation developed by \cite{Hu-Peng1995,Yong1997,Peng-Wu1999} for differential equations, we have established the well-posedness of FBVIEs.The key is to apply the chain rule to the mapping $t\mapsto\big[\int_\cdot^T\langle Y(s,s),X(s,\cdot)\rangle ds +\langle G(X(T,T)),X(T,\cdot)\rangle\big](t)$.

math.OC↗

arXiv2024

Long-Time Behavior of Zero-Sum Linear-Quadratic Stochastic Differential Games

The paper investigates the long-time behavior of zero-sum linear-quadratic stochastic differential games, aiming to demonstrate that, under appropriate conditions, both the saddle strategy and the optimal state process exhibit the exponential turnpike property. Namely, for the majority of the time horizon, the distributions of the saddle strategy and the optimal state process closely stay near certain (time-invariant) distributions $ν_1^*$, $ν_2^*$ and $μ^*$, respectively. Additionally, as a byproduct, we solve the infinite horizon version of the differential game and derive closed-loop representations for its open-loop saddle strategy, which has not been proved in the literature.

math.OC↗

arXiv2023

Present-Biased Lobbyists in Linear Quadratic Stochastic Differential Games

We investigate a linear quadratic stochastic zero-sum game where two players lobby a political representative to invest in a wind turbine farm. Players are time-inconsistent because they discount performance with a non-constant rate. Our objective is to identify a consistent planning equilibrium in which the players are aware of their inconsistency and cannot commit to a lobbying policy. We analyze the equilibrium behavior in both single player and two-player cases, and compare the behavior of the game under constant and non-constant discount rates. The equilibrium behavior is provided in closed-loop form, either analytically or via numerical approximation. Our numerical analysis of the equilibrium reveals that strategic behavior leads to more intense lobbying without resulting in overshooting.

econ.GN↗

arXiv2023

Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations with a Type of Random Coefficients

Motivated by linear-quadratic optimal control problems (LQ problems, for short) for mean-field stochastic differential equations (SDEs, for short) with the coefficients containing regime switching governed by a Markov chain, we consider an LQ problem for an SDE with the coefficients being adapted to a filtration independent of the Brownian motion driving the control system. Classical approach of completing the square is applied to the current problem and obvious shortcomings are indicated. Open-loop and closed-loop solvability are introduced and characterized.

math.OC↗

arXiv2023

A Stochastic Maximum Principle Approach for Reinforcement Learning with Parameterized Environment

In this work, we introduce a stochastic maximum principle (SMP) approach for solving the reinforcement learning problem with the assumption that the unknowns in the environment can be parameterized based on physics knowledge. For the development of numerical algorithms, we shall apply an effective online parameter estimation method as our exploration technique to estimate the environment parameter during the training procedure, and the exploitation for the optimal policy will be achieved by an efficient backward action learning method for policy improvement under the SMP framework. Numerical experiments will be presented to demonstrate that our SMP approach for reinforcement learning can produce reliable control policy, and the gradient descent type optimization in the SMP solver requires less training episodes compared with the standard dynamic programming principle based methods.

math.OC↗

arXiv2022

Multi-Dimensional Super-Linear Backward Stochastic Volterra Integral Equations

In this paper, a systematic investigation is carried out for the general solvability of multi-dimensional backward stochastic Volterra integral equations (BSVIEs) with the generators being super-linear in the adjustment variable $Z$. Two major situations are discussed: (i) When the free term is bounded with the dependence of the generator on $Z$ being of ``diagonally strictly'' quadratic growth and being sub-quadratically coupled with off-diagonal components; (ii) When the free term is unbounded having exponential moments of arbitrary order with the dependence of the generator on $Z$ being diagonally no more than quadratic and being independent of off-diagonal components. Besides, for the case that the generator is super-quadratic in $Z$, some negative results are presented.

math.PR↗

arXiv2022

Turnpike Properties for Mean-Field Linear-Quadratic Optimal Control Problems

This paper is concerned with an optimal control problem for a mean-field linear stochastic differential equation with a quadratic functional in the infinite time horizon. Under suitable conditions, including the stabilizability, the (strong) exponential, integral, and mean-square turnpike properties for the optimal pair are established. The keys are to correctly formulate the corresponding static optimization problem and find the equations determining the correction processes. These have revealed the main feature of the stochastic problems which are significantly different from the deterministic version of the theory.

math.OC↗