# Xiaowei ChenNankai University | NKU · School of Finance

Xiaowei Chen

Doctor of Philosophy

## About

34

Publications

4,156

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1,877

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Introduction

My researches focus on actuarial science, risk and uncertainty theory, decision analysis, and operations management.

**Skills and Expertise**

Additional affiliations

Education

September 2007 - June 2011

## Publications

Publications (34)

This article describes a robust continuous-time asset-liability management problem under Markov regime-switching. First, we employ the “homothetic robustness” to preserve the performance of robustness for the ALM model, which runs well in precisely modified state variables and performs reasonably if some forms of model misspecification exist. Secon...

In this paper, we build an optimal control model with the objective to maximize the expected value of the time discount utility by selecting optimal investment, liability and dividend strategies for insurance companies. We then use the techniques from Merton (J Econ Theory 3(4):373–413, 1971) to solve our optimal control problem and deduce the opti...

This paper aims to study two-factor uncertain term structure model where the volatility of the uncertain interest rate is driven by another uncertain differential equation. In order to solve this model, the nested uncertain differential equation method is employed. This paper is also devoted to the study of the numerical solutions for the proposed...

Multiobjective programming, known as multi-criteria or multi-attribute optimization, is the process of simultaneously optimizing two or more conflicting objectives. This paper aims to provide a new multiobjective programming named uncertain multiobjective programming that is a type of multiobjective programming involving uncertain variables. Some m...

Asian option is an important financial derivative instrument. It has been widely accepted by investors for its risk management property. Uncertain finance is a new field where the risk processes are described by uncertain processes. An asset price is assumed to follow a specific uncertain differential equation other than a stochastic differential e...

Other than traditional decision theory, this paper employs uncertainty theory to handle indeterminacy. Uncertain variables are used to represent uncertain choices. Uncertain expected utility function is defined as an increasing function of uncertain choices. Several mathematical properties of the uncertain expected utility functions are derived usi...

The Liu process is a new tool to deal with the noise process based on uncertainty theory. In this paper, we view the foreign exchange rate as an uncertain processes, described by uncertain differential equations driven by the Liu process, and build an uncertain currency model. Then, the uncertain currency option problems are discussed. Moreover, Eu...

A finite variation process is an uncertain process whose total variation is finite over every bounded time interval. Based on finite variation processes, a new uncertain integral is proposed in this paper. Besides, some basic properties are discussed. In the framework of uncertain integral, the uncertain differential is introduced, and the fundamen...

In this paper, several useful inequalities for uncertain variables are proved. A Borel-Cantelli lemma for uncertain measures is obtained and some convergence theorems for continuous uncertain measures are derived. Finally, these theorems are applied to compute the uncertainty distribution of Liu integral. We prove that the uncertain integral of a d...

Uncertain calculus is a branch of mathematics that deals with the integral and differential of functions of uncertain processes. This paper first introduces the Liu process as an uncertain process defined by the Liu integral. Some properties of Liu processes are investigated such as sample continuity property, finite variation property, and the fac...

Term structure models describe the evolution of the yield curve through time, without considering the influence of risk, tax, etc. Recently, uncertain processes were initialized and applied to option pricing and currency model. Under the assumption of short interest rate following uncertain processes, this study investigates the term-structure equa...

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain different...

This paper presents an uncertain stock model with periodic dividends based on uncertainty theory. Some option pricing formulae related to the proposed model are investigated and several numerical examples are discussed to illustrate the related formula.

Uncertain differential equation is a type of differential equation driven by canonical process. In this paper, a concept of α-path to uncertain differential equation is first introduced, which is a type of deterministic function that solves an associate ordinary differential equation. Then, a numerical method is designed for solving uncertain diffe...

A stationary independent increment process is an uncertain process with stationary and independent increments. This paper aims to calculate the variance of stationary independent increment processes, and gains that, for each fixed time, the variance is a constant multiplying the square of time. Based on this result, it is proved that the total vari...

ross-entropy is a measure of the difference between two distribution functions. In order to deal with the divergence of uncertain variables via uncertainty distributions, this paper aims at introducing the concept of cross-entropy for uncertain variables based on uncertain theory, as well as investigating some mathematical properties of this concep...

Project scheduling problem is to determine the schedule of allocat-ing resources so as to balance the total cost and the completion time. This paper considers a type of project scheduling problem with uncertain activity duration times. According to management goal, an uncertain programming model for this problem is proposed in this paper in which t...

In real-life projects, both the trade-off between the project cost and the project completion time, and the uncertainty of the environment are considerable aspects for decision-makers. Moreover, in some projects, activity durations show their complexity with time-dependence as well as randomness. In this paper, a stochastic time-dependent time–cost...

Uncertainty theory is a branch of mathematics of studying the subjective uncertain behavior. Entropy is a key concept which provides a quantitative measurement of the uncertainty associated with uncertain variables. In order to compute the entropy more conveniently, this paper proposes some formulas of entropy of function of uncertain variables wit...

Uncertainty theory is a branch of mathematics for modeling uncertainty in human reasoning, and uncertain statistics is a methodology for collecting and interpreting experts' experimental data by uncer-tainty theory. In this paper, we will first discuss how to collect experts' data. We apply this method to a model for estimating the distance between...

Uncertain logic is a generalization of classical logic for dealing with uncertain knowledge via uncertainty theory. The truth value is defined as the uncertain measure that a proposition is true. In this paper, a numerical method for calculating the truth value of uncertain formulas is proposed and some examples are presented.

The concept of uncertain entropy is used to provide a quantitative measurement of the uncertainty associated with uncertain variables. After introducing the definition, this paper gives some examples of entropy of uncertain variables. Furthermore this paper proposes the maximum entropy principle for uncertain variables, that is, out of all the unce...

Fuzzy differential equation is a useful tool to model a dynamical system when information about its behavior is inadequate. Different from previous works, we consider a type of fuzzy differential eqution driven by Liu process. Furthermore, we provide and prove a new existence and uniqueness theorem for fuzzy differential equations under Lipschitz c...

Option pricing is the the core content of modern finance. American option is widely accepted by investors for its flexibility of exercising time. In this paper, American option pricing formula is calculated for uncertain financial market and some mathematical properties of them are discussed. In addition, some examples are proposed.

Canonical process is a Lipschitz continuous uncertain process with stationary and independent increments, and uncertain differential
equation is a type of differential equations driven by canonical process. This paper presents some methods to solve linear
uncertain differential equations, and proves an existence and uniqueness theorem of solution f...

Uncertainty theory is a branch of mathematics to deal with subjectivity uncertainty. Uncertain variable is a measurable function defined on uncertainty space. Operations on uncertain variables is achieved through operational law. Based on the operational law, this paper proves some formulas of operational law on uncertain variables with identificat...

Based on uncertain measure, the pessimistic value and optimistic value of uncertain variables have been inroduced for handling optimization problems in uncertain environments. In this paper, some new properties of critical values of uncertain variables are investigate. equations was given. Keywords: Fuzzy variable, fuzzy difierential equation, exis...

In order to deal with the divergence of uncertain variables from a prior one, this paper is devoted to introduce the concept of cross-entropy for uncertain variables and study the minimum cross-entropy principle.

The stock model and option pricing problem are central contents in modern flnance. In this paper, generalized stock model for flnancial market is proposed and the European option pricing formula for the generalized stock model is computed.

In order to deal with the divergence of uncertain variables from a prior one, this paper is devoted to introduce the concept of cross-entropy for uncertain variables and study the minimum cross-entropy principle.

In this paper, an uncertain version of Borel-Cantelli lemma is proved. Besides, some convergence theorems of continuous uncertain measure are proposed. Using these theorems, it is proved that the uncertainty distribution function of the uncertain integral on a real function is a normal one.

## Projects

Project (1)