基于巨灾模型的巨灾保险组合研究

巨灾风险所造成的巨大损失已经威胁到人类社会的可持续发展.巨灾保险是分散巨灾损失的一种途径,利用巨灾模型研究被保风险的累积损失和个人损失分布的数学性质,且考虑损失率是巨灾强度的函数.通过巨灾模型和保险公司破产概率的计算和数值仿真,得到不能仅仅依靠保费的选择而分散巨灾风险.     

随机利率下两全保险最佳年限的确定模型

寿险模型中利率的随机性问题是近几年来保险精算学中研究的热点和重点问题。本文从降低保险公司所面临风险的角度出发,在随机利率条件下给出确定两全保险的最佳年限模型。     

Developing prospective teachers’ covariational reasoning through a model development sequence

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers’ ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented with 20 participants in a mathematical modeling course offered to prospective teachers. The participants’ developing abilities of covariational reasoning were documented under three categories: (i) identifying the variables, (ii) ways of coordinating the variables, and (iii) ways of quantifying the rate of change. The results revealed significant improvement in the prospective teachers’ ways of identifying and coordinating the variables, and in quantifying the rate of change. Moreover, the results indicated that preference for a particular way of thinking in identifying and coordinating the variables determined the prospective teachers’ way of quantifying the rate of change and thereby their level of covariational reasoning.     

A study of early career teachers’ practices related to language and language diversity during mathematics instruction

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially early career teachers’ (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students’ mathematical vocabulary use and development. Yet, there was variability in ECTs’ focus on how to teach mathematical vocabulary, expectations for students’ precise use of mathematical terminology, and the use of multiple languages during instruction. These findings indicate that ECTs need more targeted support during teacher preparation and early career teaching in order to better support all students’ language development in the mathematics classroom.     

Subitising activity relative to units construction: a case study

Subitising, a quick apprehension of the numerosity of a small set of items, has been found to change from an individual's reliance on perceptual to conceptual processes. In this study, we utilised a constructivist teaching experiment methodology to investigate how the subitising activity of one preschool student, Amy, related to her construction of prenumerical units. Subitising and counting tasks were designed to assess and perturb Amy's thinking relative to her construction of units, and to observe changes in Amy's activity associated with the different tasks. Findings indicate that as Amy's subitising activity changed from perceptual to conceptual, she constructed subitised motor units and subitised figurative units. Implications of this study suggest that the construction of subitised units may support young children's later development of arithmetic units.     

An introduction to the perplex number system

The perplex number system is a generalization of the abstract logical relationships among electrical particles. The inferential logic of the new number system is homologous to the inferential logic of the progression of the atomic numbers. An electrical progression is defined categorically as a sequence of objects with teridentities. Each identity infers corresponding values of an integer, units and a correspondence relation between each unit and its integer. Thus, in this logical system, each perplex numeral contains an exact internal representational structure; it carries an internal message. This structure is a labeled bipartite graph that is homologous to the internal electrical structure of a chemical atom. The formal logical operations are conjunctions and disjunctions. Combinations of conjunctions and disjunctions compose the spatiality of objects. Conjunctions may include the middle term of pairs of propositions with a common term, thereby creating new information. The perplex numerals are used as a universal source of diagrams.The perplex number system, as an abstract generalization of concrete objects and processes, constitutes a new exact notation for chemistry without invoking alchemical symbols. Practical applications of the number system to concrete objects (chemical elements, simple ions and molecules, and the perplex isomers, ethanol and dimethyl ether) are given. In conjunction with the real number system, the relationships between the perplex number system and scientific theories of concrete systems (thermodynamics, intra-molecular dynamics, molecular biology and individual medicine) are described.     

Budget-constrained optimal insurance with belief heterogeneity

We re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured; and in particular for singularity between these beliefs, that is, disagreement about zero-probability events. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Under a mild consistency requirement between these beliefs that is weaker than the Monotone Likelihood Ratio (MLR) condition, we characterize the optimal indemnity and show that it has a simple two-part structure: full insurance on an event to which the insurer assigns zero probability, and a variable deductible on the complement of this event, which depends on the state of the world through a likelihood ratio. The latter is obtained from a Lebesgue decomposition of the insured’s belief with respect to the insurer’s belief.     

Subgroup analysis of zero-inflated Poisson regression model with applications to insurance data

Customized personal rate offering is of growing importance in the insurance industry. To achieve this, an important step is to identify subgroups of insureds from the corresponding heterogeneous claim frequency data. In this paper, a penalized Poisson regression approach for subgroup analysis in claim frequency data is proposed. Subjects are assumed to follow a zero-inflated Poisson regression model with group-specific intercepts, which capture group characteristics of claim frequency. A penalized likelihood function is derived and optimized to identify the group-specific intercepts and effects of individual covariates. To handle the challenges arising from the optimization of the penalized likelihood function, an alternating direction method of multipliers algorithm is developed and its convergence is established. Simulation studies and real applications are provided for illustrations.     

Optimal investment of DC pension plan under short-selling constraints and portfolio insurance

In this paper we investigate an optimal investment problem under short-selling and portfolio insurance constraints faced by a defined contribution pension fund manager who is loss averse. The financial market consists of a cash bond, an indexed bond and a stock. The manager aims to maximize the expected S-shaped utility of the terminal wealth exceeding a minimum guarantee. We apply the dual control method to solve the problem and derive the representations of the optimal wealth process and trading strategies in terms of the dual controlled process and the dual value function. We also perform some numerical tests and show how the S-shaped utility, the short-selling constraints and the portfolio insurance impact the optimal terminal wealth.     

Probing interactions in exploratory teaching: a case study

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students’ competence in justifying an ellipse. We analyse the complex interactions between student, content, and teacher, and discuss explicit pedagogical strategies that help students develop a higher level of geometric reasoning. The findings indicate that students engaged in guided explorations by the teacher and in group discussions with peers were able to identify an ellipse and justify their reasoning.