Jinwu Gao

Uncertain term structure model of interest rate

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 equation. This equation is first derived for valuing zero-coupon bond. Finally, analytic solutions of the uncertain interest rate equation are given when the process of interest rate is assumed to be the uncertain counterparts of the Ho-Lee model and Vasicek model, respectively.

Some stability theorems of uncertain differential equation

Canonical process is a type of uncertain process with stationary and independent increments which are normal uncertain variables, and uncertain differential equation is a type of differential equation driven by canonical process. This paper will give a theorem on the Lipschitz continuity of canonical process based on which this paper will also provide a sufficient condition for an uncertain differential equation being stable.

Uncertain differential games with application to capitalism

AbstractUncertainty theory provides us an alternative for modeling human uncertainty without the scope of probability theory. In a dynamic game, the system dynamics often has noise by human disturbance and can be described by an uncertain differential equation. In order to investigate such a problem, an uncertain differential game model and its solution concept of feedback Nash equilibrium is proposed in this paper. Moreover, a sufficient condition is established to guarantee a feedback Nash equilibrium of the game. As an application, the capitalism problem is analyzed by uncertain differential game. The results show that uncertain differential game is a powerful tool for dealing with dynamic game.

Linear–Quadratic Uncertain Differential Game With Application to Resource Extraction Problem

Uncertain differential game investigates interactive decision making of players over time, and the system dynamics is described by an uncertain differential equation. This paper goes further to study the two-player zero-sum uncertain differential game. In order to guarantee the saddle-point Nash equilibrium, a Max-Min theorem is provided. Furthermore, when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic, the existence of saddle-point Nash equilibrium is obtained via the solvability of a corresponding Riccati equation. Finally, a resource extraction problem is analyzed by using the theory proposed in this paper.

Some Concepts and Theorems of Uncertain Random Process

To deal with a system with both randomness and uncertainty, chance theory has been built and an uncertain random variable has been proposed as a generalization of random variable and uncertain variable. Correspondingly, as a generalization of both the stochastic process and the uncertain process, this paper will propose an uncertain random process. In addition, some special types of uncertain random processes such as stationary increment process and renewal process will also be discussed.

Uncertain bimatrix game with applications

In real-world games, the players are often lack of the information about the other players’ (or even his own) payoffs. Assuming that all entries of payoff matrices are uncertain variables, this paper introduces a concept of uncertain bimatrix game. Within the framework of uncertainty theory, three solution concepts of uncertain equilibrium strategies as well as their existence theorem are proposed. Furthermore, a sufficient and necessary condition is presented for finding the uncertain equilibrium strategies. Finally, an example is provided for illustrating the usefulness of the theory developed in this paper.

Uncertain Shapley value of coalitional game with application to supply chain alliance

Uncertain coalitional game deals with situations in which the transferable payoffs are uncertain variables. The uncertain core has been proposed as the solution of uncertain coalitional game. This paper goes further by presenting two definitions of uncertain Shapley value: expected Shapley value and α-optimistic Shapley value. Meanwhile, some characterizations of the uncertain Shapley value are investigated. Finally, as an application, uncertain Shapley value is used to solve a profit allocation problem of supply chain alliance.

Bayesian equilibria for uncertain bimatrix game with asymmetric information

In an uncertain bimatrix game, there are two solution concepts of

The modes of convergence in the approximation of fuzzy random optimization problems

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