Robust non-zero-sum investment and reinsurance game with default risk

This paper investigates a non-zero-sum stochastic differential game between two competitive CARA insurers, who are concerned about the potential model ambiguity and aim to seek the robust optimal reinsurance and investment strategies. The ambiguity-averse insurers are allowed to purchase reinsurance treaty to mitigate individual claim risks; and can invest in a financial market consisting of one risk-free asset, one risky asset and one defaultable corporate bond. The objective of each insurer is to maximize the expected exponential utility of his terminal surplus relative to that of his competitor under the worst-case scenario of the alternative measures. Applying the techniques of stochastic dynamic programming, we derive the robust Nash equilibrium reinsurance and investment policies explicitly and present the corresponding verification theorem. Finally, we perform some numerical examples to illustrate the influence of model parameters on the equilibrium reinsurance and investment strategies and draw some economic interpretations from these results.     

区域合作减排策略选择及提升对策研究

跨区域合作的碳减排是实现减排目标较为有效的机制。通过构建政府间减排演化博弈模型,模拟了区域内地方政府独立减排、合作减排情形的策略选择演化过程。研究发现,(1)当区域内本地政府和外部政府经济发展水平都比较低时,无论是独立减排还是合作减排,{减排,减排}都是地方政府的稳定选择策略,但减排效果不显著;(2)独立减排情形下,经济先发地区减排意愿薄弱,后发地区有减排意愿,但减排效果并不显著;(3)合作减排时,当协同收益小于交易成本时,随着地方政府经济发展,减排系统博弈最终会向地方政府一方减排一方不减排的方向演进;当协同收益大于交易成本时,通过合作减排,实现了资源的优势互补,降低了碳排放的负外部效应,提高了减排意愿。最后提出通过搭建起区域合作交流平台,激发地方政府减排活力及推进低碳经济发展等建议,来提高协同收益或降低交易成本,有效促进区域合作减排。     

L-凸空间中的新的极大元定理及其对对策平衡的应用

在L-凸空间中建立了新的极大元定理.作为应用,获得了L-凸空间中抽象经济和定性对策的平衡存在定理.     

具有模糊支付的模糊合作对策中局中人间的相互影响

基于郭嗣琮[19～21]提出的关于模糊数的限制运算,本文探讨了具有模糊支付的模糊合作对策中局中人间的相互影响问题。给出了局中人间相互影响的表达式。当所给模糊合作对策具有相互独立性和k-单调性时,论述了一些基本性质。通过对Shapley函数概念的推广,得到相应的模糊Shapley度量指标。并对所给指标满足的性质进行了研究。最后通过算例分析来说明所给指标有效性和实用性。     

The Shapley–Shubik index for simple games with multiple alternatives

When analyzing mathematically decision mechanisms ruled by voting it is sometimes convenient to include abstention as a possible alternative for the voters. In classical simple games, abstention, if considered, is formally equivalent to voting against the proposal. Simple games with alternatives are useful to study voting systems where abstention does not favour any of the options. In this work, we axiomatically characterize the Shapley–Shubik index for simple games with alternatives and apply it to an example taken from real life. This work has been partially supported by Grant MTM 2006–06064 of the Education and Science Spanish Ministry and the European Regional Development Fund, and Grant SGR 2005–00651 of the Catalonia Government.     

Weighted Banzhaf power and interaction indexes through weighted approximations of games

The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo-Boolean functions. Considering certain weighted versions of this approximation problem, we define a class of weighted interaction indexes that generalize the Banzhaf interaction index. We show that these indexes define a subclass of the family of probabilistic interaction indexes and study their most important properties. Finally, we give an interpretation of the Banzhaf and Shapley interaction indexes as centers of mass of this subclass of interaction indexes.     

Two‐objective optimization strategies using the adjoint method and game theory in inverse natural convection problems

This paper considers the problem of estimating the strengths of two time‐varying heat sources simultaneously, from measurements of the temperature inside the square domain in a porous medium, when prior knowledge of the source functions is not available. This problem is an inverse natural convection problem. In order to circumvent this problem, we define several optimization criteria (objective functionals) that measure discrepancies between model and measured data, where objective functionals depend on two heat sources and use multi‐criteria optimization to identify Nash equilibria, which are solutions to the non‐cooperative game according to game theory. Two non‐cooperative game strategies are considered: competitive (Nash) game and hierarchical (modified Stackelberg) game. The methodology that we employ relies on a combination of mixed finite element space approximations, finite difference time discretizations, adjoint equation and sensitivity equation techniques, and nonlinear conjugate gradient algorithms for the solutions of estimating two heat sources. Applying the Sobolev gradient for the noise removal is investigated. The performance of the present technique of inverse analysis is evaluated, by means of several numerical experiments, and is found to be very accurate as well as efficient. Copyright © 2012 John Wiley & Sons, Ltd.     

补贴退坡-双积分政策下两级供应链生产决策优化分析

在退坡与双积分政策下, 分析由一个车企和一个分销商组成的两级供应链中的生产决策问题。基于Stackelberg博弈, 阐释退坡和双积分对车企与分销商最优决策的影响。对比分析集中决策和分散决策对供应链绩效的影响, 帮助汽车供应链有效适应“双积分”政策。研究表明:在双积分政策未实施时, 随着补贴的不断降低, 新能源汽车的需求量、车企的利润会随之降低; 双积分政策实施之后, 车企不断提高研发努力水平可使新能源汽车的需求量提高, 车企与分销商的利润可获得帕累托改进。数值分析表明, 双积分政策可以有效促进新能源汽车的发展。     

成渝地区双城经济圈核心城市的博弈分析与对策研究——以交通物流基础设施建设为例

推进成渝地区双城经济圈建设已经上升为国家发展战略.以交通物流基础设施建设为例,从个体理性和团体理性两个方面,对竞争状态、合作状态和混合状态三种情况分别构建博弈关系模型并求解,得出结论:在成渝地区双城经济圈建设交通物流基础设施的过程中,核心城市的个体利益大于团体利益,表现为个体理性与团体理性之间的冲突,即两者存在非合作博弈关系.最后针对核心城市存在的非合作博弈关系,提出促进成渝地区双城经济圈核心城市协同发展的对策建议.