Many researchers have proposed restoration techniques incorporating the concept of k-shortest disjoint paths in survivable WDM (Wavelength Division Multiplexing) optical networks, but without considering network perfo...
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Many researchers have proposed restoration techniques incorporating the concept of k-shortest disjoint paths in survivable WDM (Wavelength Division Multiplexing) optical networks, but without considering network performance and network costs simultaneously. In this paper we need to carefully look into how well the concept of shortest disjoint paths is incorporated for given objective functions. Seven objective functions and four algorithms are presented to evaluate the concept of k-shortest disjoint paths for the design of a robust WDM optical network. A case study based on simulation experiments is conducted to illustrate the application and efficiency of k-shortest disjoint paths in terms of following objective goals: minimal wavelengths, minimal wavelength link distance, minimal wavelength mileage costs, even distribution of traffic flows, average restoration time of backup lightpaths, and physical topology constraints.
Many researchers have proposed restoration techniques incorporating the concept of k-shortest disjoint paths in survivable WDM (Wavelength Division Multiplexing) optical networks, but without considering network perfo...
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Many researchers have proposed restoration techniques incorporating the concept of k-shortest disjoint paths in survivable WDM (Wavelength Division Multiplexing) optical networks, but without considering network performance and network costs simultaneously. In this paper we need to carefully look into how well the concept of shortest disjoint paths is incorporated for given objective functions. Seven objective functions and four algorithms are presented to evaluate the concept of k-shortest disjoint paths for the design of a robust WDM optical network. A case study based on simulation experiments is conducted to illustrate the application and efficiency of k-shortest disjoint paths in terms of following objective goals: minimal wavelengths, minimal wavelength link distance, minimal wavelength mileage costs, even distribution of traffic flows, average restoration time of backup lightpaths, and physical topology constraints.
In this paper, one kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond (bank account) and in a real project which has the production. The ...
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In this paper, one kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond (bank account) and in a real project which has the production. The bank pays at an interest rate for any deposit and takes at a large rate for any loan. The optimal strategies are obtained by Hamilton-Jacobi-Bellman equation which is derived from dynamic programming principle. We also give the economic analysis to the optimal choice using the investment theory. For the specific Hyperbolic Absolute Risk Aversion case, we get the explicit optimal investment and consumption solution. At last, we give some simulation results to illustrate the optimal result and the influence of the volatility parameter on the optimal choice. (c) 2005 Elsevier Inc. All rights reserved.
We study a zero-sum differential game with hybrid controls in which both players are allowed to use continuous as well as discrete controls. Discrete controls act on the system at a given set interface. The state of t...
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We study a zero-sum differential game with hybrid controls in which both players are allowed to use continuous as well as discrete controls. Discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, an autonomous jump set A or a controlled jump set C, where one controller can choose to jump or not. At each jump, the trajectory can move to a different Euclidean space. One player uses all the three types of controls, namely, continuous controls, autonomous jumps, and controlled jumps;the other player uses continuous controls and autonomous jumps. We prove the continuity of the associated lower and upper value functions V- and V+. Using the dynamic programming principle satisfied by V- and V+, we derive lower and upper quasivariational inequalities satisfied in the viscosity sense. We characterize the lower and upper value functions as the unique viscosity solutions of the corresponding quasivariational inequalities. Lastly, we state an Isaacs like condition for the game to have a value.
We study here the impulse control problem in infinite as well as finite horizon. We allow the cost functionals and dynamics to be unbounded and hence the value function can possibly be unbounded. We prove that the val...
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We study here the impulse control problem in infinite as well as finite horizon. We allow the cost functionals and dynamics to be unbounded and hence the value function can possibly be unbounded. We prove that the value function is the unique viscosity solution in a suitable subclass of continuous functions, of the associated quasivariational inequality. Our uniqueness proof for the infinite horizon problem uses stopping time problem and for the finite horizon problem, comparison method. However, we assume proper growth conditions on the cost functionals and the dynamics. (c) 2005 Elsevier Inc. All rights reserved.
One kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond (bank account) and in a real project which has the production. The bank pays at an...
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ISBN:
(纸本)9787810778022
One kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond (bank account) and in a real project which has the production. The bank pays at an interest rate for any deposit and takes at a large rate for any loan. The optimal strategies are obtained by Hamilton-Jacobi-Bellman equation which is derived from dynamic programming principle. We also give the economic analysis to the optimal choice using the investment theory. For the specific Hyperbolic Absolute Risk Aversion case, we get the explicit optimal investment and consumption solution. At last, we give some simulation results to illustrate the optimal result and the influence of the volatility parameter on the optimal choice.
＜正＞One kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond （bank account） and in a real project which has the production. The bank pa...
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＜正＞One kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond （bank account） and in a real project which has the production. The bank pays at an interest rate for any deposit and takes at a large rate for any loan. The optimal strategies are obtained by Hamilton-Jacobi-Bell-man equation which is derived from dynamic programming principle. We also give the economic analysis to the optimal choice using the investment theory. For the specific Hyperbolic Absolute Risk Aversion case, we get the explicit optimal investment and consumption solution. At last, we give some simulation results to illustrate the optimal result and the influence of the volatility parameter on the optimal choice.
Motivated by the work of Fleming [6], we provide a general framework to associate inf-sup type values with the Isaacs equations. We show that upper and lower bounds for the generators of inf-sup type are upper and low...
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Motivated by the work of Fleming [6], we provide a general framework to associate inf-sup type values with the Isaacs equations. We show that upper and lower bounds for the generators of inf-sup type are upper and lower Hamiltonians, respectively. In particular, the lower (resp. upper) bound corresponds to the progressive (resp. strictly progressive) strategy. By the dynamic programming principle and identification of the generator, we can prove that the inf-sup type game is characterized as the unique viscosity solution of the Isaacs equation. We also discuss the Isaacs equation with a Hamiltonian of a convex combination between the lower and upper Hamiltonians.
We consider that the reserve of an insurance company follows a Cramer-Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a dynamic choice of both t...
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We consider that the reserve of an insurance company follows a Cramer-Lundberg process. The management has the possibility of controlling the risk by means of reinsurance. Our aim is to find a dynamic choice of both the reinsurance policy and the dividend distribution strategy that maximizes the cumulative expected discounted dividend payouts. We study the usual cases of excess-of-loss and proportional reinsurance as well as the family of all possible reinsurance contracts. We characterize the optimal value function as the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation and we prove that there exists an optimal band strategy. We also describe the optimal value function for small initial reserves.
We investigate a model of hybrid control system in which both discrete and continuous controls are involved. In this general model, discrete controls act on the system at a given set interface. The state of the system...
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We investigate a model of hybrid control system in which both discrete and continuous controls are involved. In this general model, discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where the controller can choose to jump or not. At each jump, the trajectory can move to a different Euclidean space. We prove the continuity of the associated value function V with respect to the initial point. Using the dynamic programming principle satisfied by V, we derive a quasi-variational inequality satisfied by V in the viscosity sense. We characterize the value function V as the unique viscosity solution of the quasi-variational inequality by the comparison principle method.
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