Constructing Examples with 5 Equilibria for Symmetric 3 × 2 Ces / Les Pure Exchange Economies

This paper explores the existence of multiple equilibria for symmetric 3 individual, 2 good CES / LES pure exchange economies. Analytically, we show that there are no more than 5 equilibria in such economies. The number of equilibria varies from 5 to 3 then to 1. We generalize our analytical results of existence of 1, 3, 5 equilibria for a wide range of parametrizations. We also provide concrete examples of 1, 3, 5 equilibria with parameter zones specified.     

On the distribution of exponential functionals for Lévy processes with jumps of rational transform

We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Lévy processes with rational Laplace exponent. This extends recent results by Cai and Kou [3] on the processes with hyper-exponential jumps.     

Exponentially-fitted methods and their stability functions

We investigate the properties of stability functions of exponentially-fitted Runge–Kutta methods, and we show that it is possible (to some extent) to determine the stability function of a method without actually constructing the method itself. To focus attention, examples are given for the case of one-stage methods. We also make the connection with so-called integrating factor methods and exponential collocation methods. Various approaches are given to construct these methods.     

Magnus integrators for solving linear-quadratic differential games

We consider Magnus integrators to solve linear-quadratic N$N$-player differential games. These problems require to solve, backward in time, non-autonomous matrix Riccati differential equations which are coupled with the linear differential equations for the dynamic state of the game, to be integrated forward in time. We analyze different Magnus integrators which can provide either analytical or numerical approximations to the equations. They can be considered as time-averaging methods and frequently are used as exponential integrators. We show that they preserve some of the most relevant qualitative properties of the solution for the matrix Riccati differential equations as well as for the remaining equations. The analytical approximations allow us to study the problem in terms of the parameters involved. Some numerical examples are also considered which show that exponential methods are, in general, superior to standard methods.     

Sequentially two-leveled egalitarianism for TU games: Characterization and application

A new linear value for cooperative transferable utility games is introduced. The recursive definition of the new value for an n-person game involves a sequential process performed at n − 1 stages, applying the value to subgames with a certain size k,1 ? k < n, combining with the rule of two-leveled egalitarianism (additive normalization) in order to guarantee the efficiency property for the new value, sequentially two-leveled egalitarianism, shortly S₂EG value, applied to subgames of size k + 1. The new value will be characterized in various ways. The S₂EG value differs from the Shapley value since, besides efficiency, linearity, and symmetry, it verifies an additional property with respect to so-called scale-dummy player (replacing dummy player property). Consequently, the S₂EG value of a game may be determined as the solidarity value of the per-capita game (incorporating the proportional rule due to different levels of efficiency). Various potential representations of the new value are established. In the application to a land corn production economy, it yields allocations, in which the landlord’s interest coincides with striving for a maximum production level. For economies with the linear production function, not only the unique landlord but also all the workers have incentives to increase the scale of the economy.     

Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by ??-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiplepriors utility and the technique of backward stochastic differential equations (BSDEs), we transform the ??-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor??s uncertainty. Our model investigates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flexibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.     

Robust exponential stability of impulsive switched systems with switching delays: A Razumikhin approach

In this paper, we focus on the robust exponential stability of a class of uncertain nonlinear impulsive switched systems with switching delays. We introduce a novel type of piecewise Lyapunov-Razumikhin functions. Such functions can efficiently eliminate the impulsive and switching jump of adjacent Lyapunov functions at impulsive switching instants. By Razumikhin technique, the delay-independent criteria of exponential stability are established on the minimum dwell time. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained theoretical results.     

Exponential synchronization of fuzzy cellular neural networks with mixed delays and general boundary conditions

In this paper, we study exponential synchronization of delayed reaction-diffusion fuzzy cellular neural networks with general boundary conditions. By using Sobolev inequality techniques and constructing suitable Lyapunov functional, some sufficient conditions are given to ensure the exponential synchronization of the drive-response delayed fuzzy cellular neural networks with general boundary conditions. Finally, an example is given to verify the theoretical analysis.     

Optimal reinsurance–investment problem in a constant elasticity of variance stock market for jump‐diffusion risk model

In this paper, we consider the jump‐diffusion risk model with proportional reinsurance and stock price process following the constant elasticity of variance model. Compared with the geometric Brownian motion model, the advantage of the constant elasticity of variance model is that the volatility has correlation with the risky asset price, and thus, it can explain the empirical bias exhibited by the Black and Scholes model, such as volatility smile. Here, we study the optimal investment–reinsurance problem of maximizing the expected exponential utility of terminal wealth. By using techniques of stochastic control theory, we are able to derive the explicit expressions for the optimal strategy and value function. Numerical examples are presented to show the impact of model parameters on the optimal strategies. Copyright © 2011 John Wiley & Sons, Ltd.     

Positive almost periodic solution for a class of Nicholson’s blowflies model with a linear harvesting term

In this paper, we study the problem of positive almost periodic solutions for the generalized Nicholson’s blowflies model with a linear harvesting term and multiple time-varying delays. By applying the fixed point theorem and the Lyapunov functional method, we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results.