Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

The fundamental theorem of mutual insurance

The essence of mutual insurance is the notion that re-distributing risk in a pool of risks is more beneficial than taking the risk alone. Interpreting ‘more beneficial’ as an increase in utility and considering sequences of exchangeable risks, we are able to formalize this notion from the policyholder’s perspective and demonstrate its validity for various alternative preference functionals (e.g., expected utility, Choquet expected utility, and distortion risk measures). To obtain this result, we exploit that for a sequence of exchangeable risks the corresponding sequence of arithmetical averages is a reversed martingale.We conclude that pooling risks is fundamental for understanding the mechanisms of insurance because it favourably affects the utility of policyholders, and we refer to this phenomenon as the ‘utility-improving effect of risk pooling’. Moreover, we demonstrate that the utility of the policyholder is (strictly) increasing with the size of the risk pool.     

Utility maximization problem with random endowment and transaction costs: when wealth may become negative

In this article, we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct a shadow market by the dual optimal process and consider the utility-based pricing for random endowment.     

Optimal proportional reinsurance with common shock dependence

In this paper, we consider the optimal proportional reinsurance strategy in a risk model with multiple dependent classes of insurance business, which extends the work of Liang and Yuen (2014) to the case with the reinsurance premium calculated under the expected value principle and to the model with two or more classes of dependent risks. Under the criterion of maximizing the expected exponential utility, closed-form expressions for the optimal strategies and value function are derived not only for the compound Poisson risk model but also for the diffusion approximation risk model. In particular, we find that the optimal reinsurance strategies under the expected value premium principle are very different from those under the variance premium principle in the diffusion risk model. The former depends not only on the safety loading, time and interest rate, but also on the claim size distributions and the counting processes, while the latter depends only on the safety loading, time and interest rate. Finally, numerical examples are presented to show the impact of model parameters on the optimal strategies.     

A model of product line design and introduction sequence with reservation utility

Cannibalization is a major concern for a firm when designing a product line. In addition, external options from outside the firm’s product line may also play a significant role. In this paper, we investigate the impact of external options, represented by reservation utility, on product line design and introduction sequence. We find that: (a) heterogeneous reservation utility defines the relative attractiveness of segments and corresponding product line; (b) reservation utility makes it more favorable to introduce products sequentially rather than simultaneously; (c) aggregating segments is an effective way to mitigate cannibalization when it becomes too difficult to manage with different values of reservation utility across multiple segments; and (d) introducing products in a non-monotone order of quality can improve profit from simultaneous introduction when the value of reservation utility of a middle segment is particularly high.     

绿色建筑项目管理综合均衡优化研究

绿色建筑凭借其诸多优点,已然成为我国未来建筑发展的新方向,而对绿色建筑的工期、成本和功能进行全面系统研究并进行综合均衡优化,对于促进绿色建筑的发展具有深远影响.在描述各工程活动的成本和持续时间之间、功能和持续时间之间的非线性关系基础上,运用多属性效用函数理论构建了绿色建筑项目的功能一工期一成本综合均衡优化模型,并用遗传算法进行求解,可以得到最佳均衡解.最后通过一个实例验证了优化模型具有良好的科学性和实用性.     

ON EQUILIBRIUM PRICING AS CONVEX OPTIMIZATION

We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets： 1. A mixed Fisher and Arrow- Debreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex opti- mization by an interior-point algorithm in polynomial time.     

Optimal investment with transaction costs based on exponential utility function: a parabolic double obstacle problem

This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.     

Risk-sensitive dynamic pricing for a single perishable product

We show that the monotone structures of dynamic pricing for a single perishable product under risk-neutrality are preserved under risk-sensitivity with the additive general utility and atemporal exponential utility functions. We also show that the optimal price is decreasing over the degree of risk-sensitivity under the exponential class of both additive and atemporal utility functions.     

Incomplete financial markets and contingent claim pricing in a dual expected utility theory framework

This paper investigates the price for contingent claims in a dual expected utility theory framework, the dual price, considering arbitrage-free financial markets. A pricing formula is obtained for contingent claims written on n underlying assets following a general diffusion process. The formula holds in both complete and incomplete markets as well as in constrained markets. An application is also considered assuming a geometric Brownian motion for the underlying assets and the Wang transform as the distortion function.