A new existence result for second-order BSDEs with quadratic growth and their applications

In this paper, we study a class of second-order backward stochastic differential equations with quadratic growth in coefficients. In particular, we provide an existence result for these equations and give their applications by solving robust utility maximization problems and introducing a type of nonlinear evaluations.     

高校收费和招生改革的社会影响的博弈模型分析

针对我国高校近年来不断扩大招生规模,提高收费标准等一系列改革举措,本文用微观经济分析的方法,通过建立相应的博弈模型,具体分析了这一系列改革对学生的影响.主要结论一是高校扩招(或提高学费)增大了学生读书的机会成本,同时降低了读书的效用,但只要学生读书的效用严格大于不读的效用,高校就有动力扩大招生或提高学费);二是扩招和提高学费对学生的影响具有动态相对性,其影响力的大小与现阶段二者的相对水平有关;三是在一定条件下扩大招生规模尤其是提高收费水平会使经济条件不同的学生在是否深造和是否选择名校或热门专业上作出完全不同的抉择,产生了教育公平问题.此外还得到了关于高校改革对其自身收益影响的一些结论.     

Utilization of mathematical programming for public systems: An application to effective formation of integrated regional information networks

This paper concerns a methodological reflection on the multiobjective approach to public systems which involve group decision processes. Particular attention is given to an integrated program of regional systems which include value trade-offs between multiple objectives. Our intention is to combine the judgmental processes with the optimization processes in the soft public systems. A two-layer approach is applied. At the first layer, each regional program is formulated in mathematical programming based on a utility assessment with different regional characteristics. Each subsystem independently reflects its particular concern as a single agent. The dual optimal solutions obtained for each subsystem are treated as an index, or the theoretical prices, representing the value trade-offs among the multiple objectives. At the second layer, an effective formation of interregional cooperation for compromising the conflicting regional interests is examined. Ann-person cooperative game in the characteristic function form is used to evaluate the effectiveness of the cooperation. The characteristic function for the game is derived on the incremental value of the regional benefit after the formation of a cooperation. The nucleolus and the augmented nucleolus as the solution concepts of the cooperative game are used for indicating the effectiveness of the cooperation. Finally using alternative criteria, the results in assessing the best decisions are examined comparatively.     

Weighted Banzhaf values

The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values.     

Revisiting the problem of integrability in utility theory

We revisit the problem of integrability in the consumer theory, focusing on the main difficulties. First, we look for a neat and simple local existence result, and then for a global solution. Second, observing that a utility function (or indirect utility function) cannot be determined uniquely, we propose a means to get a kind of uniqueness result. Our approach is coordinate-free and can be used both in the classical case of a finite-dimensional commodity space and in the case an infinite-dimensional model is adopted.     

Worst portfolios for dynamic monetary utility processes

We study the worst portfolios for a class of law invariant dynamic monetary utility functions with domain in a class of stochastic processes. The concept of comonotonicity is introduced for these processes in order to prove the existence of worst portfolios. Using robust representations of monetary utility function processes in discrete time, a relation between the worst portfolios at different periods of time is presented. Finally, we study conditions to achieve the maximum in the representation theorems for concave monetary utility functions that are continuous for bounded decreasing sequences.     

Aggregation of utility-based individual preferences for group decision-making

Multi-attribute utility theory (MAUT) elicits an individual decision maker’s preferences for single attributes and develops a utility function by mathematics formulation to add up the preferences of the entire set of attributes when assessing alternatives. A common aggregation method of MAUT for group decisions is the simple additive weighting (SAW) method, which does not consider the different preferential levels and preferential ranks for individual decision makers’ assessments of alternatives in a decision group, and thus seems too intuitive in achieving the consensus and commitment for group decision aggregation. In this paper, the preferential differences denoting the preference degrees among different alternatives and preferential priorities denoting the favorite ranking of the alternatives for each decision maker are both considered and aggregated to construct the utility discriminative values for assessing alternatives in a decision group. A comparative analysis is performed to compare the proposed approach to the SAW model, and a satisfaction index is used to investigate the satisfaction levels of the final two resulting group decisions. In addition, a feedback interview is conducted to understand the subjective perceptions of decision makers while examining the results obtained from these two approaches for the second practical case. Both investigation results show that the proposed approach is able to achieve a more satisfying and agreeable group decision than that of the SAW method.     

Optimal Exponential Utility in a Jump Bond Market

We consider the optimal exponential utility in a bond market with jumps basing on a model similar to Björk et al. [4 Björk , T. , Kabanov , Y. , and Runggaldier , W. 1997 . Bond market structure in the presence of marked point processes . Math. Finance 7 : 211 – 223 .[Crossref], [Web of Science ®] , [Google Scholar]], which is arbitrage free. Similar to the normalized integral with respect to the cylindrical martingale first introduced in Mikulevicius and Rozovskii [13 Mikulevicius , R. , and Rozovskii , B.L. 1998 . Normalized stochastic integrals in topological vector spaces . In : Séminaire de probabilités XXXII (Lecture Notes in Mathematics) . Springer , Berlin , pp. 137 – 165 . [Google Scholar]], we introduce the (𝕄, Q ⁰)-normalized martingale and local (𝕄, Q ⁰)-normalized martingale. For a given maturity T ₀ ∈ [0, T*], we describe the minimal entropy martingale (MEM) based on [T ₀, T*] by a backward semimartingale equation (BSE) w.r.t. the (𝕄, Q ⁰)-normalized martingale. Then we give an explicit form of the optimal approximate wealth to the optimal exp-utility problem by making use of the solution of the BSE. Finally, we describe the dynamics of the exp utility indifference valuation of a bounded contingent claim H ∈ L ^∞(? _{T 0} ) by another BSE under the minimal entropy martingale measure in the incomplete market.     

随机波动率市场存在股票误价时的最优投资策略

本文研究了随机波动率市场中存在股票误价(mispricing)时的最优投资组合选择问题.假设投资者的目标是最大化终端财富的期望幂效用;其可投资于无风险资产、市场指数和两支相同权益或近似度极高的股票,其中至少有一支股票存在误价;市场收益的波动率和股票系统风险由Heston随机波动率模型刻画.运用动态规划方法和Lagrange乘子法,分别得到不存在/存在有限卖空约束时,投资者的最优投资策略及最优值函数的解析式,并通过理论分析和数值算例,阐述了投资时间水平和价格随机误差对最优投资策略的影响.