arXiv subjects

Jie Xiong

Publications and source records attributed to Jie Xiong.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Annuitization, Consumption, and Investment with Costly Capital Injections

We study a joint optimal decision of portfolio, consumption, and annuitization for a pension-plan manager who balances retirement consumption benefits against the cost of maintaining the solvency of pension account. The pension sponsor provides costly capital injection to prevent negative wealth. Annuity purchases are irreversible, and injected funds remain in the liquid account and earn interest. Using the Legendre transform, we derive a semi-explicit solution to the associated free-boundary problem and verify the optimality of the resulting strategies. We identify an endogenous annuity-income threshold separating injection-active and injection-inactive regions and characterize six policy regimes arising from the interplay between capital injections and consumption constraints. Compared with the no-injection benchmark, capital injections delay annuitization, alter the structure of the annuitization boundary, and permit positive holdings in risky assets even at zero liquid wealth. Numerical results further reveal that cheaper annuities may increase the expected capital contributions required from the pension sponsor.

math.OC↗

arXiv2026

Turnpike Properties for Exploratory Stochastic Linear-Quadratic Optimal Control with Indefinite Cost Functionals

Continuous-time exploratory stochastic control provides a stochastic control framework for the exploration--exploitation trade-off in reinforcement learning. In this paper, we study the long-time behavior of finite-horizon exploratory stochastic linear-quadratic (LQ) optimal control problems as the time horizon $T\to\infty$, and establish so-called turnpike properties for such problems. In the finite-horizon setting, we derive a feedback representation of the exploratory stochastic LQ problem and analyze its long-time structure. We formulate an exploratory static distribution optimization problem analogous to the classical static optimization problem and identify the corresponding static reference object. We prove a turnpike property for the optimal state process relative to a stochastic reference process, as well as a Wasserstein turnpike property for the optimal control distribution. In addition to the exploratory control formulation, another key feature of our results is that, by introducing a joint coercivity condition, we allow the cost functional to be indefinite and the controlled state system to be merely stabilizable. Consequently, the derived turnpike property is novel even within the classical stochastic LQ control framework.

math.OC↗

arXiv2026

Strong well-posedness for cyclic catalytic reaction--diffusion SPDEs with mutation and immigration

We study cyclic catalytic stochastic reaction-diffusion systems with mutation and immigration. The equations have square-root catalytic coefficients and spatially colored noise. Under a condition requiring the cyclic inward drift to dominate the corresponding noise covariance, we establish global strong well-posedness for nonnegative initial states. Our approach combines positivity-preserving approximations, uniform energy estimates, and a concave power entropy that controls the occupation of states near zero. These boundary estimates allow us to derive a Hellinger stability inequality for two synchronized weak variational solutions, yielding pathwise uniqueness directly in this solution class. We then use joint compactness of the approximating solutions and their driving noise, together with martingale identification and the Gyongy-Krylov criterion, to construct a probabilistically strong solution on the prescribed Wiener space.

math.PR↗

arXiv2026

Backward stochastic partial differential equations with unbounded random coefficients

We study a linear backward stochastic partial differential equation with unbounded observation-adapted random coefficients, motivated by the duality approach to nonlinear filtering. The coefficients depend predictably on the observation history through a control with almost surely finite time-integrated squared norm. The drift, diffusion, and coefficient multiplying the martingale integrand may grow linearly in space. The diffusion matrix may grow quadratically in space and is allowed to be degenerate. Under bounded positive-order spatial derivatives and bounded smooth observation-measurable terminal data, we prove existence and uniqueness in a polynomially weighted Sobolev class up to control-energy stopping times. The proof combines conditional parameter estimates, entropy bounds for likelihoods, stability under the reference probability, and stochastic-flow reconstruction.

math.PR↗

arXiv2026

Stochastic Riccati equations with jumps for indefinite linear-quadratic control: A stochastic value-flow approach

This paper studies the nonlinear matrix-valued stochastic Riccati equation with jumps (SRE-J) arising from indefinite stochastic linear-quadratic optimal control problems with random coefficients and Poisson jumps. We demonstrate that the presence of jumps may cause the matrix-valued optimal state process $\mathbf{X}$ to become singular, even under the standard condition. Consequently, the classical representation $P=\mathbf{Y}\mathbf{X}^{-1}$ used in the diffusion case is generally unavailable. To overcome this difficulty, we construct the Riccati process directly from the stochastic value flow under the uniform convexity condition on the cost functional, an approach that requires no invertibility condition on the jump coefficient. We then prove that the SRE-J admits a maximal strongly regular solution, which yields a closed-loop representation of the unique open-loop optimal control. Furthermore, we establish verifiable sufficient conditions for uniform convexity and provide examples of indefinite stochastic linear-quadratic problems with jumps.

math.OC↗

arXiv2026

Partially Observed McKean--Vlasov Control with Vanishing Observation Intensities

We study partially observed McKean--Vlasov jump-diffusions with controlled counting intensities that may vanish and depend on the unconditional physical state distribution. A deterministic upper bound on the likelihood supports one-sided state--likelihood variations, a smooth-test-function expansion of the physical state marginal, and a necessary maximum principle without inverse intensity or likelihood terms. We also establish a one-sided total-variation derivative of the physical probability on the fixed noise space, including a nonnegative singular component on baseline-null histories. A quadratic example shows, within a specified policy family and under explicit conditions, that positive variance feedback raises the first-order activation fee threshold while negative feedback lowers it.

math.OC↗

arXiv2026

Invariant Measures for Interacting Continuous-State Population Models

We study invariant probabilities for nonlinear two-population branching systems with competition, cooperation, or predator--prey interaction, driven by Brownian noise and spectrally positive stable jumps. Without immigration, every invariant probability of a conservative competitive or predator--prey system is concentrated on the boundary under either boundary convention. With nontrivial axis dynamics, coordinatewise continuation admits only the point mass at the origin. For cooperative systems, we give criteria for boundary concentration and interior stationarity, including a sharp criterion for bilinear cooperation with a common relative noise exponent. With immigration, explicit parameter conditions yield existence and stationary moment bounds. For square-root diffusions with positive immigration, these conditions ensure interior concentration and full support on the closed quadrant. Further lower bounds on immigration rates give uniqueness and convergence of time-averaged transition laws.

math.PR↗

arXiv2026

PnPSelect: Plug-and-play IoT Device Selection Using Ultra-wideband Signals

In recent years, the number of Internet of Things (IoT) devices in smart homes has rapidly increased. A key challenge affecting user experience is how to enable users to efficiently and intuitively select the devices they wish to control. This paper proposes PnPSelect, a plug-and-play IoT device selection solution utilizing Ultra-wideband (UWB) technology on commercial devices. Unlike previous works, PnPSelect does not require the installation of dedicated hardware on each IoT device, thereby reducing deployment costs and complexities, and achieving true plug-and-play functionality. To enable intuitive device selection, we introduce a pointing direction estimation method that utilizes UWB readings from a single anchor to infer the user pointing direction. Additionally, we propose a lightweight device localization method that allows users to register new IoT devices by simply pointing at them from two distinct positions, eliminating the need for manual measurements. We implement PnPSelect on commercial smartphones and smartwatches and conduct extensive evaluations in both controlled laboratory settings and real-world environments. Our results demonstrate high accuracy, robustness, and adaptability, making PnPSelect a practical and scalable solution for next-generation smart home interactions.

cs.HC↗

arXiv2026

Uniqueness and stability of nonlinear filtering equations with unbounded random coefficients

We study a multidimensional nonlinear filtering model whose coefficients depend on a given observation-adapted predictable process and whose observation drift may grow linearly in both the state and the random input. Due to the unboundedness of the observation drift, a global reference measure is not available. To overcome this hurdle, a localized entropy argument is adapted to prove the stopped likelihood to be a uniformly integrable martingale at each control-energy stopping level. The stopped Zakai equation, and hence, the stopped filtering equation is derived. The global filtering equation is then established by de-localization. The uniqueness of the solution to the stopped Zakai equation is obtained by a duality backward stochastic partial differential equation. This uniqueness then propagates to that of the global filtering equation through the stopped ones. Finally, a stability result is established in $W_1$-distance of measures.

math.PR↗

arXiv2026

Stochastic linear-quadratic control problem for regime-switching jump-diffusion system and its application to finance

This paper investigates a stochastic linear-quadratic (SLQ) control problem for a regime-switching jump-diffusion system. Unlike traditional regime-switching diffusion systems that couple a diffusion process with a Markov chain, we incorporate the jumps of the Markov chain into the state equation. This modeling methodology effectively captures potential gains or losses of the system during the regime transitions. It should be noted that the introduction of Markov chain jumps into the state equation leads to increased complexity in the corresponding coupled differential Riccati equations (CDREs), thereby rendering the solvability of the control problem more challenging. Under the assumption that the cost functional is uniformly convex, we establish the unique solvability of the corresponding CDREs. Building upon this foundation, we derive a closed-loop representation for the unique open-loop optimal control. Finally, we apply our theoretical results to the mean-variance portfolio selection problem in a regime-switching financial market with Markov chain jumps and obtain its efficient frontier.

math.OC↗

arXiv2026

A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations

This paper studies a partially observed stochastic optimal control problem for jump-diffusion states observed through multivariate counting processes with state-dependent intensities. Because the observation jumps carry information about the latent state through their intensities, the variational analysis involves coupled state and likelihood-ratio perturbations. By introducing a reference probability measure and augmenting the state with the counting-process likelihood ratio, we establish a stochastic maximum principle whose first-order necessary condition is expressed as a conditional Hamiltonian stationarity relation with respect to the observation filtration. Finally, an LQ example is used to examine the compatibility of a linear adjoint ansatz and to illustrate numerically the coupled partial-information stationarity system.

math.OC↗

arXiv2026

Behaviors near infinity for mutually enhancing continuous-state population dynamics

In this paper we consider a two-dimensional generalized continuous-state branching process with mutually enhancing two-way interactions characterized by two stochastic differential equations driven by Brownian motions and spectrally positive $α$-stable random measures. Such continuous-state population dynamics can also be identified as a stochastic Lotka-Volterra type population model. Infinite behavior such as explosion/nonexplosion for this population and staying infinite/coming down from infinity are derived under various conditions on the coefficients involved in the model and the conclusions are rather sharp

math.PR↗

arXiv2026

Extinction behaviour for mutually enhancing continuous-state population dynamics

In this paper, we study a two-dimensional process arising as the unique nonnegative solution to a system of two stochastic differential equations (SDEs) with mutually enhancing two-way interactions driven by independent Brownian motions and spectrally positive $α$-stable random measures. Such a SDE system can be identified as a continuous-state Lotka-Volterra type population model. Extinction properties of the populations are studied for different choices of the coefficients involved in the SDEs.

math.PR↗

arXiv2026

Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients

We study pathwise uniqueness for cyclic catalytic stochastic differential equations whose state-dependent square-root diffusion coefficients are non-Lipschitz and degenerate on the boundary. The approach is the direct construction of a strong solution using a Malliavin compactness criterion. The key is the development of a new family of boundary-sensitive weighted Malliavin estimates for the tangent processes of the smooth approximations. Pathwise uniqueness then follows from the dual Yamada-Watanabe argument together with the weak uniqueness available in the literature.

math.PR↗

arXiv2026

Continuous-time q-learning for Markov regime switching system under Tsallis entropy

This paper studies continuous-time q-learning (the continuous-time counterpart of Q-learning) for a Markov regime-switching system under Tsallis entropy regularization. The Tsallis entropy regularization yields an optimal policy distribution that may not necessarily be a Gibbs measure, thereby complicating algorithm design. Furthermore, to address the limited universality of current continuous-time regime-switching reinforcement learning algorithms (often restricted to the exploratory mean-variance framework), this study focuses on continuous-time q-learning for Markov regime-switching systems based on Tsallis entropy, aiming for a more universally applicable continuous-time reinforcement learning method. We establish the martingale characterization of the q-function under Tsallis entropy for continuous-time Markov regime-switching systems. We further design two q-learning algorithms that differ based on whether the Lagrange multiplier can be explicitly derived. We apply these algorithms to the continuous-time exploratory mean-variance portfolio optimization problem in a regime-switching market. Numerical experiments demonstrate the satisfactory performance of our q-learning algorithms.

math.OC↗

arXiv2026

Extinction and extinguishment properties for a nonlinear predator-prey branching model

We study extinction and extinguishment in a two-type continuous-state nonlinear branching model driven by Brownian branching noise and spectrally positive stable jumps. The populations are subject to nonlinear self-regulation and a mixed-sign predator--prey interaction: the second promotes the first, whereas the first suppresses the second. Two complementary structures are developed. An exact power--logarithmic cancellation functional removes the interaction drifts and yields stochastic Lyapunov estimates, nonexplosion, and boundary criteria. In the multiplicative regimes, integrating-factor identities and geometric Lévy factorizations express extinction through weighted exposure clocks and reduce the long-time analysis to effective decay rates. These methods yield almost-sure extinction criteria and identify a regime in which finite-time extinction and nonextinction coexist. On nonextinction, both populations remain positive at all finite times and converge jointly to zero, exhibiting joint extinguishment rather than positive persistence.

math.PR↗

arXiv2026

Saturation-Aware Predictive Quantization for Low-Power ECG Acquisition: A Benchmark of Taylor, Adaptive-Order, Kalman, and LSTM Predictors

Wearable electrocardiogram (ECG) monitors require energy-efficient analog-to-digital converters (ADCs), yet conventional successive-approximation-register (SAR) ADCs repeatedly resolve slowly varying most significant bits. Predictive quantization (PQ) instead estimates the next sample and quantizes only the residual, thereby reducing the required conversion depth. Its principal failure mode is residual saturation, which occurs when prediction error exceeds the residual ADC range and is irreversibly clipped. We compared four one-step-ahead predictors under a common 10-bit, saturation-aware PQ model with residual widths from 2 to 8 bits. The benchmark included first-order Taylor extrapolation, an adaptive-order predictor, a constant-velocity Kalman filter, and a two-layer long short-term memory (LSTM) network. We used an open-loop protocol in which all predictors received past original samples. This protocol isolates intrinsic prediction performance from recursive reconstruction-error propagation. Saturation rate (SR) was the primary metric, complemented by overflow energy ratio (OER), which weights each event by its squared overflow depth. On a 5,317-sample excerpt from MIT-BIH Arrhythmia Database Record 101, the Kalman predictor performed best at Br=6. It achieved 30.88 dB SNR, 2.16% SR, and 12.93% OER, compared with 28.39 dB, 2.69%, and 25.29% for Taylor extrapolation. The adaptive-order predictor achieved 29.61 dB SNR and 2.44% SR using three registers, two comparators, and no multiplier. The LSTM reached 29.28 dB SNR and did not outperform the model-based predictors on this limited-data benchmark. Under the evaluated excerpt and open-loop protocol, Br=6 provided a favorable balance between reconstruction fidelity and conversion depth. Closed-loop, multi-subject, and hardware validation are required before system-level energy or deployment claims can be made.

eess.SP↗

arXiv2026

Closed-loop solvability of infinite-horizon stochastic linear-quadratic problem for Markov regime-switching jump-diffusion system

This paper investigates a class of stochastic linear-quadratic (SLQ) control problems over an infinite horizon for Markov regime-switching jump-diffusion systems. Unlike classical diffusion models modulated by a Markov chain, we assume that the state process undergoes abrupt jumps that are synchronous with the regime switches of the Markov chain. In contrast to conventional Poisson jump-diffusion models, the jumps in the state process are entirely induced by the state transitions of the Markov chain, which can be interpreted as losses or gains of state process incurred during regime changes. Under this formulation, we thoroughly discuss the closed-loop solvability of the SLQ control problem and provide a feedback representation of the optimal control via the stabilizing solution of a system of coupled algebraic Riccati equations (CAREs). Finally, we further apply our results to a lifetime wealth tracking problem and derive the corresponding optimal investment strategy.

math.OC↗