arXiv subjects

Xiaoshan Chen

Publications and source records attributed to Xiaoshan Chen.

7 recordsLinked to original sources

arXiv2025

Pricing Model for Data Assets in Investment-Consumption Framework with Ambiguity

Data assets are data commodities that have been processed, produced, priced, and traded based on actual demand. Reasonable pricing mechanism for data assets is essential for developing the data market and realizing their value. Most existing literature approaches data asset pricing from the seller's perspective, focusing on data properties and collection costs, however, research from the buyer's perspective remains scarce. This gap stems from the nature of data assets: their value lies not in direct revenue generation but in providing informational advantages that enable enhanced decision-making and excess returns. This paper addresses this gap by developing a pricing model based on the informational value of data assets from the buyer's perspective. We determine data asset prices through an implicit function derived from the value functions in two robust investment-consumption problems under ambiguity markets via the indifference pricing principle. By the existing research results, we simplify the value function, using mathematical analysis and differential equation theory, we derive general expressions for data assets price and explore their properties under various conditions. Furthermore, we derive the explicit pricing formulas for specific scenarios and provide numerical illustration to describe how to use our pricing model.

q-fin.MF↗

arXiv2024

Optimal consumption under a drawdown constraint over a finite horizon

This paper studies a finite horizon utility maximization problem on excessive consumption under a drawdown constraint. Our control problem is an extension of the one considered in Bahman et al. (2019) to the model with a finite horizon and an extension of the one considered in Jeon and Oh (2022) to the model with zero interest rate. Contrary to Bahman et al. (2019), we encounter a parabolic nonlinear HJB variational inequality with a gradient constraint, in which some time-dependent free boundaries complicate the analysis significantly. Meanwhile, our methodology is built on technical PDE arguments, which differs from the martingale approach in Jeon and Oh (2022). Using the dual transform and considering the auxiliary variational inequality with gradient and function constraints, we establish the existence and uniqueness of the classical solution to the HJB variational inequality after the dimension reduction, and the associated free boundaries can be characterized in analytical form. Consequently, the piecewise optimal feedback controls and the time-dependent thresholds for the ratio of wealth and historical consumption peak can be obtained.

math.OC↗

arXiv2022

Hard Exudate Segmentation Supplemented by Super-Resolution with Multi-scale Attention Fusion Module

Hard exudates (HE) is the most specific biomarker for retina edema. Precise HE segmentation is vital for disease diagnosis and treatment, but automatic segmentation is challenged by its large variation of characteristics including size, shape and position, which makes it difficult to detect tiny lesions and lesion boundaries. Considering the complementary features between segmentation and super-resolution tasks, this paper proposes a novel hard exudates segmentation method named SS-MAF with an auxiliary super-resolution task, which brings in helpful detailed features for tiny lesion and boundaries detection. Specifically, we propose a fusion module named Multi-scale Attention Fusion (MAF) module for our dual-stream framework to effectively integrate features of the two tasks. MAF first adopts split spatial convolutional (SSC) layer for multi-scale features extraction and then utilize attention mechanism for features fusion of the two tasks. Considering pixel dependency, we introduce region mutual information (RMI) loss to optimize MAF module for tiny lesions and boundary detection. We evaluate our method on two public lesion datasets, IDRiD and E-Ophtha. Our method shows competitive performance with low-resolution inputs, both quantitatively and qualitatively. On E-Ophtha dataset, the method can achieve $\geq3\%$ higher dice and recall compared with the state-of-the-art methods.

eess.IV↗

arXiv2018

Properties of Switching Jump Diffusions: Maximum Principles and Harnack Inequalities

This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated operators for switching jump diffusions are non-local, resulting in more difficulty in treating such systems. Our study is carried out by taking into consideration of the interplay of stochastic processes and the associated systems of integro-differential equations.

math.PR↗

arXiv2018

Recurrence and Ergodicity for A Class of Regime-Switching Jump Diffusions

This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying processes feature in the switching process depends on the jump diffusions. In this paper, conditions for recurrence and positive recurrence are derived. Ergodicity is examined in detail. Existence of invariant probability measures is proved.

math.PR↗

arXiv2017

The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic Equations

We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally Hölder continuous with exponent $δ\in (0, 1]$, the stochastic solution, which represents the price of a European option, is shown to be a classical solution to the Cauchy problem. This improves the standard requirement $δ\ge 1/2$. Uniqueness results, including a Feynman-Kac formula and a comparison theorem, are established without assuming the usual linear growth condition on the diffusion coefficient. When the stochastic solution is not smooth, it is characterized as the limit of an approximating smooth stochastic solutions. In deriving the main results, we discover a new, probabilistic proof of Kotani's criterion for martingality of a one-dimensional diffusion in natural scale.

math.PR↗

arXiv2011

Indifference Pricing of American Option Underlying Illiquid Stock under Exponential Forward Performance

This work focuses on the indifference pricing of American call option underlying a non-traded stock, which may be partially hedgeable by another traded stock. Under the exponential forward measure, the indifference price is formulated as a stochastic singular control problem. The value function is characterized as the unique solution of a partial differential equation in a Sobolev space. Together with some regularities and estimates of the value function, the existence of the optimal strategy is also obtained. The applications of the characterization result includes a derivation of a dual representation and the indifference pricing on employee stock option. As a byproduct, a generalized Ito's formula is obtained for functions in a Sobolev space.

q-fin.PR↗