A method based on cumulative prospect theory was proposed to solve risky multiple attribute decision making problems with Four -dimensional reference points. Considering the influence of different learning processes a...A method based on cumulative prospect theory was proposed to solve risky multiple attribute decision making problems with Four -dimensional reference points. Considering the influence of different learning processes and corresponding features on decision-making, a new reference-learning behavior is added, and a risk-based multiple-attribute decision-making method based on four-dimensional reference point cumulative prospect theory is proposed. Firstly, according to the cumulative prospect theory, the prospect value and the decision function value of the four reference points of learning, time, evaluation value and expected value are calculated respectively, and the cumulative prospect value matrix of each program dynamic is formed. Secondly,according to the WAA operalor, Maximize the stage weighting model to obtain the integrated cumulative prospect value. Finally, on the basis of this, the alternatives are sorted according to the size of the total cumulative prospect value, and compared with other methods, the validity and scientific of the proposed method are proved.展开更多
We consider the compound binomial model in a Markovian environment presented by Cossette et al.(2004). We modify the model via assuming that the company receives interest on the surplus and a positive real-valued prem...We consider the compound binomial model in a Markovian environment presented by Cossette et al.(2004). We modify the model via assuming that the company receives interest on the surplus and a positive real-valued premium per unit time, and introducing a control strategy of periodic dividend payments. A Markov decision problem arises and the control objective is to maximize the cumulative expected discounted dividends paid to the shareholders until ruin minus a discounted penalty for ruin. We show that under the absence of a ceiling of dividend rates the optimal strategy is a conditional band strategy given the current state of the environment process. Under the presence of a ceiling for dividend rates, the character of the optimal control strategy is given. In addition, we offer an algorithm for the optimal strategy and the optimal value function.Numerical results are provided to illustrate the algorithm and the impact of the penalty.展开更多
This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total l...This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system.展开更多
文摘A method based on cumulative prospect theory was proposed to solve risky multiple attribute decision making problems with Four -dimensional reference points. Considering the influence of different learning processes and corresponding features on decision-making, a new reference-learning behavior is added, and a risk-based multiple-attribute decision-making method based on four-dimensional reference point cumulative prospect theory is proposed. Firstly, according to the cumulative prospect theory, the prospect value and the decision function value of the four reference points of learning, time, evaluation value and expected value are calculated respectively, and the cumulative prospect value matrix of each program dynamic is formed. Secondly,according to the WAA operalor, Maximize the stage weighting model to obtain the integrated cumulative prospect value. Finally, on the basis of this, the alternatives are sorted according to the size of the total cumulative prospect value, and compared with other methods, the validity and scientific of the proposed method are proved.
基金supported by Hunan Provincial Natural Science Foundation of China(Grant No.14JJ2069)National Natural Science Foundation of China(Grant Nos.6127229411171101 and11371301)
文摘We consider the compound binomial model in a Markovian environment presented by Cossette et al.(2004). We modify the model via assuming that the company receives interest on the surplus and a positive real-valued premium per unit time, and introducing a control strategy of periodic dividend payments. A Markov decision problem arises and the control objective is to maximize the cumulative expected discounted dividends paid to the shareholders until ruin minus a discounted penalty for ruin. We show that under the absence of a ceiling of dividend rates the optimal strategy is a conditional band strategy given the current state of the environment process. Under the presence of a ceiling for dividend rates, the character of the optimal control strategy is given. In addition, we offer an algorithm for the optimal strategy and the optimal value function.Numerical results are provided to illustrate the algorithm and the impact of the penalty.
基金supported by National Natural Science Foundation of China(Grant Nos.61374067 and 11471341)
文摘This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system.
