In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theor...In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theorem of generalized minimax regret equilibrium point with scalar set payoffs holds. In other words, when the scalar set payoffs functions and feasible constraint mappings are slightly disturbed, by using Fort theorem and continuity results of set-valued mapping optimal value functions, we obtain a general stability theorem for generalized minimax regret equilibria with scalar set payoffs. At the same time, an example is given to illustrate our result.展开更多
In optimal wind bidding strategy related literatures, it is usually assumed that the full distribution information (for example, the cumulative distribution function or the probability density function) of wind power ...In optimal wind bidding strategy related literatures, it is usually assumed that the full distribution information (for example, the cumulative distribution function or the probability density function) of wind power output is known. In real world applications, however, only very limited distribution information can be obtained. Therefore, the “optimal bidding strategy” obtained based on the hypothetical distribution may be far away from the true optimal one. In this paper, an optimal bidding strategy is obtained based on the minimax regret criterion. The salient feature of the new approach is that it requires only partial information of wind power distribution, for example, the expectation and the support set. Numerical test is then performed and the results suggest that the method established in this paper is effective.展开更多
We consider a room allocation problem for a hotel providing room reservation service through multiple channels.Traditional room allocation models usually assume hotels can forecast the characteristics of demand functi...We consider a room allocation problem for a hotel providing room reservation service through multiple channels.Traditional room allocation models usually assume hotels can forecast the characteristics of demand function and/or arrival process to some extent.But in practice,such a restrictive assumption is possibly unrealistic,and thus the corresponding risk-neutral approaches are debatable.The main contribution of this paper is that we formulate the hotel’s room allocation problem without any assumption on demand from the perspective of minimax regret and derive an adaptive nested limits strategy which allows higher profitable channels having access to all rooms reserved for lower profitable channels.Our results show that customers arrive in a low-before-high manner in the worst-case scenarios.On this basis,we further prove the lower bound of maximum regret for any strategy and develop an optimal strategy matching the lower bound.Comparison with other common strategies is also discussed.展开更多
Critical systems are typically complex systems that are required to perform reliably over a wide range of scenarios, or multistate world. Seldom does a single system exist that performs best for all plausible scenario...Critical systems are typically complex systems that are required to perform reliably over a wide range of scenarios, or multistate world. Seldom does a single system exist that performs best for all plausible scenarios. A robust solution, one that performs relatively well over a wide range of scenarios, is often the preferred choice for reduced risk at an acceptable cost. The alternative with the maximum expected utility may possess vulnerabilities that could be exploited. The best strategy is likely to be a hybrid solution. The von Neumann-Morgenstern Expected Utility Theory (EUT) would never select such a solution because, given its linear functional form, the expected utility of a hybrid solution cannot be greater than that of every constituent alternative. The continuity axiom and the independence axiom are assessed to be unrealistic for the problem of interest. Several well-known decision models are analyzed and demonstrated to be potentially misleading. The linear disappointment model modifies EUT by adding a term proportional to downside risk;however, it does not provide a mathematical basis for determining preferred hybrid solutions. The paper proposes a portfolio allocation model with stochastic optimization as a flexible and transparent method for defining choice problems and determining hybrid solutions for critical systems with desirable properties such as diversification and robustness.展开更多
文摘In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theorem of generalized minimax regret equilibrium point with scalar set payoffs holds. In other words, when the scalar set payoffs functions and feasible constraint mappings are slightly disturbed, by using Fort theorem and continuity results of set-valued mapping optimal value functions, we obtain a general stability theorem for generalized minimax regret equilibria with scalar set payoffs. At the same time, an example is given to illustrate our result.
文摘In optimal wind bidding strategy related literatures, it is usually assumed that the full distribution information (for example, the cumulative distribution function or the probability density function) of wind power output is known. In real world applications, however, only very limited distribution information can be obtained. Therefore, the “optimal bidding strategy” obtained based on the hypothetical distribution may be far away from the true optimal one. In this paper, an optimal bidding strategy is obtained based on the minimax regret criterion. The salient feature of the new approach is that it requires only partial information of wind power distribution, for example, the expectation and the support set. Numerical test is then performed and the results suggest that the method established in this paper is effective.
基金supported by National Natural Science Foundation of China[grant number 71501045],[grant number 71701048]Natural Science Foundation of Fujian Province[grant number 2016J01332]+1 种基金ProgramforNew Century Excellent Talents in Fujian Province Universityand Special Foundation for Science and Technology Innovation of Fujian Agriculture and Forestry University.
文摘We consider a room allocation problem for a hotel providing room reservation service through multiple channels.Traditional room allocation models usually assume hotels can forecast the characteristics of demand function and/or arrival process to some extent.But in practice,such a restrictive assumption is possibly unrealistic,and thus the corresponding risk-neutral approaches are debatable.The main contribution of this paper is that we formulate the hotel’s room allocation problem without any assumption on demand from the perspective of minimax regret and derive an adaptive nested limits strategy which allows higher profitable channels having access to all rooms reserved for lower profitable channels.Our results show that customers arrive in a low-before-high manner in the worst-case scenarios.On this basis,we further prove the lower bound of maximum regret for any strategy and develop an optimal strategy matching the lower bound.Comparison with other common strategies is also discussed.
文摘Critical systems are typically complex systems that are required to perform reliably over a wide range of scenarios, or multistate world. Seldom does a single system exist that performs best for all plausible scenarios. A robust solution, one that performs relatively well over a wide range of scenarios, is often the preferred choice for reduced risk at an acceptable cost. The alternative with the maximum expected utility may possess vulnerabilities that could be exploited. The best strategy is likely to be a hybrid solution. The von Neumann-Morgenstern Expected Utility Theory (EUT) would never select such a solution because, given its linear functional form, the expected utility of a hybrid solution cannot be greater than that of every constituent alternative. The continuity axiom and the independence axiom are assessed to be unrealistic for the problem of interest. Several well-known decision models are analyzed and demonstrated to be potentially misleading. The linear disappointment model modifies EUT by adding a term proportional to downside risk;however, it does not provide a mathematical basis for determining preferred hybrid solutions. The paper proposes a portfolio allocation model with stochastic optimization as a flexible and transparent method for defining choice problems and determining hybrid solutions for critical systems with desirable properties such as diversification and robustness.
