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Shuzhen Yang

Publications and source records attributed to Shuzhen Yang.

At least 19 recordsLinked to original sources
arXiv2026

Pareto frontier of portfolio investment under volatility uncertainty and short-sale constraints market

In this paper, we investigate a portfolio investment problem under volatility uncertainty and short-sale constraints market via sublinear expectation which is used to model volatility uncertainty. We assume the stocks admit volatility uncertainty. Thus the related portfolio has upper variance (maximum risk) and lower variance (minimum risk). By introducing a risk factor $w$ to conduct coupled modeling of the maximum and minimum risks, a simplified Sublinear Expectation Mean-Uncertainty Variance (SLE-MUV) model is constructed. Theoretically, we show that the Pareto frontier of the SLE-MUV model is a continuous convex curve, and its optimal solution can be expressed as a polynomial analytical expression with respect to the risk factor $w$. Empirically, we systematically test the practical performance of the SLE-MUV model and conduct comparative analysis with the traditional Mean-Variance (MV) model as the benchmark based on three sets of samples -- simulated generated data, data of the US stock market and the A-share market. The empirical results show that the SLE-MUV model can significantly improving the risk-adjusted return of the investment portfolio.

q-fin.MF↗
arXiv2026

Robust linear regression under latent group heterogeneity

Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we consider a linear regression model where the random intercept term has mean uncertainty and the error term has variance uncertainty. We develop a novel two-step approach, named Expectation-Maximization with Moving Block (EMMB), to estimate the model parameters. The proposed method requires no prior knowledge of group structures or change points. Theoretical properties of the estimators are established under mild regularity conditions. Simulation studies and a real-data application to PM2.5 concentration modeling in Beijing demonstrate the superiority of the proposed method: it captures substantial intercept heterogeneity overlooked by ordinary least squares and yields more accurate and interpretable estimates.

math.ST↗
arXiv2025

Infinite Anticipation Backward Stochastic Differential Equations

In this paper, we introduce a new type of backward stochastic differential equations (BSDEs) with infinite anticipation, where the generator depends on the entire future values of the solution in infinite horizon. We show that the new BSDEs has a unique solution and admits a comparison result. In the end, we solve a stochastic control problem via a duality between BSDEs with infinite anticipation and stochastic differential equations (SDEs) with infinite delay.

math.PR↗
arXiv2025

Early-stopping for Transformer model training

This work, based on Random Matrix Theory (RMT), introduces a novel early-stopping strategy for Transformer training dynamics. Utilizing the Power Law (PL) fit to tansformer attention matrices as a probe, we demarcate training into three stages: structural exploration, heavy-tailed structure stabilization, and convergence saturation. Empirically, we observe that the spectral density of the shallow self-attention matrix $V$ consistently evolves into a heavy-tailed distribution. Crucially, we propose two consistent and validation-set-free criteria: a quantitative metric for heavy-tailed dynamics and a novel spectral signature indicative of convergence. The strong alignment between these criteria highlights the utility of RMT for monitoring and diagnosing the progression of Transformer model training.

cs.LG↗
arXiv2025

Minimum-Time Stochastic Optimal Control Problems Under Mean Constraints and Application to Portfolio Investment

Motivated by the practical demand for minimum-time optimal investment problems, we develop a unified framework for mean constraints minimum-time stochastic optimal control problems. In this setting, the minimum-time criterion is defined as the expected earliest time to reach a target state, making the terminal time dependent on the control. The main contributions of this work are twofold: first, we derive an extended stochastic maximum principle for the proposed model and further prove the existence of an optimal control for the linear systems; second, we establish a bang-bang type optimal control for the linear time-optimal control problem. In the end, we solve a financial portfolio optimization problem within the proposed framework.

math.OC↗
arXiv2025

A robust and p-hacking-proof significance test under variance uncertainty

P-hacking poses challenges to traditional hypothesis testing. In this paper, we propose a robust method for the one-sample significance test that can protect against p-hacking from sample manipulation. Precisely, assuming a sequential arrival of the data whose variance can be time-varying and for which only lower and upper bounds are assumed to exist with possibly unknown values, we use the modern theory of sublinear expectation to build a testing procedure which is robust under such variance uncertainty, and can protect the significance level against potential data manipulation by an experimenter. It is shown that our new method can effectively control the type I error while preserving a satisfactory power, yet a traditional rejection criterion performs poorly under such variance uncertainty. Our theoretical results are well confirmed by a detailed simulation study.

math.ST↗
arXiv2024

Stochastic maximum principle for optimal control problem with varying terminal time and non-convex control domain

In this paper, we consider a varying terminal time structure for the stochastic optimal control problem under state constraints, in which the terminal time varies with the mean value of the state. In this new stochastic optimal control system, the control domain does not need to be convex and the diffusion coefficient contains the control variable. To overcome the difficulty in the proof of the related Pontryagin's stochastic maximum principle, we develop asymptotic first- and second-order adjoint equations for the varying terminal time, and then establish its variational equation. In the end, two examples are given to verify the main results of this study.

math.OC↗
arXiv2024

Asset pricing under model uncertainty with discrete time and states

In this study, we consider the asset pricing under model uncertainty with discrete time and states structure. For the single-period securities model, we give a novel definition of arbitrage under a family of probability, and explore of its relationship with risk neutral probability measure. Focusing on the financial market with short sales prohibitions, we separately investigate the necessary and sufficient conditions for no-arbitrage asset pricing based on nonlinear expectation which composed with a family of probability. When each linear expectation driven by the probability in the family of probability becomes a martingale measure, the necessary and sufficient conditions are same, which coincide with the existing results. Furthermore, we expand the main results of single-period securities model to the case of multi-period securities model. By-product, we obtain the superhedging prices of contingent claim under model uncertainty.

q-fin.MF↗
arXiv2024

Uncertainty in the financial market and application to forecastabnormal financial fluctuations

The integration and innovation of finance and technology have gradually transformed the financial system into a complex one. Analyses of the causesd of abnormal fluctuations in the financial market to extract early warning indicators revealed that most early warning systems are qualitative and causal. However, these models cannot be used to forecast the risk of the financial market benchmark. Therefore, from a quantitative analysis perspective, we focus on the mean and volatility uncertainties of the stock index (benchmark) and then construct three early warning indicators: mean uncertainty, volatility uncertainty, and ALM-G-value at risk. Based on the novel warning indicators, we establish a new abnormal fluctuations warning model, which will provide a short-term warning for the country, society, and individuals to reflect in advance.

q-fin.RM↗
arXiv2024

Sublinear expectation structure under countable state space

In this study, we propose the sublinear expectation structure under countable state space. To describe an interesting "nonlinear randomized" trial, based on a convex compact domain, we introduce a family of probability measures under countable state space. Corresponding the sublinear expectation operator introduced by S. Peng, we consider the related notation under countable state space. Within the countable state framework, the sublinear expectation can be explicitly calculated by a novel repeated summation formula, and some interesting examples are given. Furthermore, we establish Monotone convergence theorem, Fatou's lemma and Dominated convergence theorem of sublinear expectation. Afterwards, we consider the independence under each probability measure, upon which we establish the sublinear law of large numbers and obtain the maximal distribution under sublinear expectation.

math.PR↗
arXiv2023

Parameter learning: stochastic optimal control approach with reinforcement learning

In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an appropriate cost functional, based on a classical optimal feedback control, we translate the original optimal control problem to a new control problem which takes place the unknown parameter as control, and the related optimal control can be used to estimate the unknown parameter. We establish the mathematical framework of the dynamic equation for the exploratory state, which is consistent with the existing results. Furthermore, we consider the linear stochastic differential equation case where the drift or diffusion term with unknown parameter. Then, we investigate the general case where both the drift and diffusion terms contain unknown parameters. For the above cases, we show that the optimal density function satisfies a Gaussian distribution which can be used to estimate the unknown parameter. Based on the obtained estimation of the parameters, we can do empirical analysis for a given model.

math.OC↗
arXiv2023

Stochastic maximum principle for recursive optimal control problems with varying terminal time

This paper introduces a new recursive stochastic optimal control problem driven by a forward-backward stochastic differential equations (FBSDEs), where the ter?minal time varies according to the constraints of the state of the forward equation. This new optimal control problem can be used to describe the investment portfolio problems with the varying investment period. Based on novel \r{ho}-moving variational and adjoint equations, we establish the stochastic maximum principle for this optimal control problem including the classical optimal control problem as a particular case. Furthermore, we propose an example to verify our main results.

math.OC↗
arXiv2023

Fixed-point iterative algorithm for SVI model

The stochastic volatility inspired (SVI) model is widely used to fit the implied variance smile. Presently, most optimizer algorithms for the SVI model have a strong dependence on the input starting point. In this study, we develop an efficient iterative algorithm for the SVI model based on a fixed-point and least-square optimizer. Furthermore, we present the convergence results in certain situations for this novel iterative algorithm. Compared with the quasi-explicit SVI method, we demonstrate the advantages of the fixed-point iterative algorithm using simulation and market data.

q-fin.MF↗
arXiv2022

Extended Dynamic Programming Principle and Applications to Time-Inconsistent Control

Since Peng (1993) established a local maximum principle for a general stochastic control problem governed by forward-backward stochastic differential equations (FBSDEs), the corresponding partial differential equation (PDE) characterization has not been developed yet. The main difficulty stems from the potential time inconsistency inherent in this class of control problems. In a dimension-augmented space, we first establish an extended dynamic programming principle (DPP). Consequently, an extended Hamilton-Jacobi-Bellman (HJB) equation is derived. The existence and uniqueness of a new type of viscosity solution is also investigated for this extended HJB equation. Compared to extant research on the stochastic maximum principle, the present paper is the first normal work on the PDE method for a control system with states evolving in both forward and backward manners. Interestingly, our extended DPP provides an equilibrium solution for general time-inconsistent control problems associated with the traditional mean-variance model, risk-sensitive control and utility optimization for narrow framing investors, among others.

math.OC↗
arXiv2021

A compensatory model for quantile estimation and application to VaR

Unlike the standard two-step workflow of estimating a time series distribution and extracting quantiles from it, this paper proposes a compensatory model to refine quantile estimates based on an existing fitted distribution. We embed a new penalty term in the model and theoretically characterize its ability to bound realized coverage errors, yielding an adaptive quantile estimator. Backtests on the S&P 500 and NASDAQ Composite show that the compensatory model substantially reduces unconditional coverage errors across four VaR estimators: all 16 compensatory model forecasts pass the unconditional coverage test, compared with 7 of the 16 corresponding Base forecasts. The conditional-calibration results remain estimator-dependent, indicating that compensatory model is a coverage-correction layer rather than a replacement for conditional-tail modelling.

q-fin.MF↗
arXiv2021

$L^p$ estimations of fully coupled FBSDEs

In this study, for any given terminal time $T$, we establish an $L^p$ ($P>2$) estimations of fully coupled FBSDEs based on the $L^2$ estimations. Yong [24] proposed that a natural question is whether an adapted $L^2$-solution is an adapted $L^p$ solution for some $p>2$. In this study, we give a positive answer to this question. For any given terminal time $T$, based on an observation of the relation between $L^2$ and $L^p$ estimations of FBSDEs, we prove that a unique $L^2$-solution of fully coupled FBSDEs is an $L^p$-solution under standard conditions on the coefficients. Furthermore, we show that the fully coupled FBSDEs developed in the linear quadratic optimal control problem or investigated by the "decoupling random field" method admit a unique $L^p$-solution.

math.PR↗
arXiv2021

Linear regression under model uncertainty

We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined and changing according to a mechanism unknown to the statistician. By following the recent theory of sublinear expectation, we propose to characterize such mean and variance uncertainty in the response variable by two specific nonlinear random variables, which encompass an infinite family of probability distributions for the response variable in the sense of (linear) classical probability theory. The approach enables a family of estimators under various loss functions for the regression parameter and the parameters related to model uncertainty. The consistency of the estimators is established under mild conditions on the data generation process. Three applications are introduced to assess the quality of the approach including a forecasting model for the S\&P Index.

math.ST↗