Evaluation of firm’s loss due to incomplete information in real investment decision

We investigate the effect of incomplete information in a model where a start-up with a unique idea and technology pioneers a new market but will eventually be expelled from the market by a large firm’s subsequent entry. We evaluate the start-up’s loss due to incomplete information about the large firm’s behavior. We clarify conditions under which the start-up needs more information about the large firm. The proposed method of evaluating the loss due to incomplete information could also be applied to other real options models involving incomplete information.     

Karl Menger's contributions to social thought

The work of Karl Menger in social science is briefly surveyed, in particular in the areas of marginal utility and diminishing value, utility, and uncertainty, a logic of imperatives based on deterrence, and a theory of voluntary associations in which cohesive groups are studied combinatorially.     

The utility of deductibles from the insurer's point of view

The relationship between the premiums for deductible cover and for full cover are analyzed with respect to the utility for the insurer. Theorem 1 shows that within natural bounds for the premiums neither form of coverage is generally preferred by all insurers. Theorems 2–4 indicate that in many realistic cases a deductible cover requires a higher risk loading factor by the insurer than a full insurance cover. Theorem 2(b) also contains an exception to this rule.     

投资决策中信息服务的研究

在一定假设条件下,建立了投资者对信息服务的价值分析和最佳投资的理论模型,并对文[1]中的结论进行修正,得到了与实际更加符合的结论.     

George Dantzig’s contributions to integer programming

This paper reviews George Dantzig’s contributions to integer programming, especially his seminal work with Fulkerson and Johnson on the traveling salesman problem.     

On the loss of information due to fuzziness in experimental observations

The absence of exactness in the observation of the outcomes of a random experiment always entails a loss of information about the experimental distribution. This intuitive assertion will be formally proved in this paper by using a mathematical model involving the notions of fuzzy information and fuzzy information system (as intended by Tanaka, Okuda and Asai) and Zadeh's probabilistic definition. On the basis of this model we are first going to consider a family of measures of information enclosing some well-known measures, such as those defined by Kagan, Kullback-Leibler and Matusita, and then to establish methods for removing the loss of information due to fuzziness by increasing suitably the number of experimental observations.     

Informational aspects of a class of subjective games of incomplete information: Static case

Subjective games of incomplete information are formulated where some of the key assumptions of Bayesian games of incomplete information are relaxed. The issues arising because of the new formulation are studied in the context of a class of nonzero-sum, two-person games, where each player has a different model of the game. The static game is investigated in this note. It is shown that the properties of the static subjective game are different from those of the corresponding Bayesian game. Counterintuitive outcomes of the game can occur because of the different beliefs of the players. These outcomes may lead the players to realize the differences in their models.This work was sponsored by the Office of Naval Research under Contract No. N00014-84-C-0485.     

Computing the value of information of quadratic decision problems and its non-negativity conditions

Abstract

There are many examples in the literature of non-cooperative games in which players prefer not to have additional information in order to improve their payoff. We present a general quadratic game in which, if one of the players improves his payoff upon obtaining more information, the other player’s payoff worsens in such a way that there is a net social loss due to having more information. How can we ensure this does not occur? The results of this paper are (1) the mathematical expression of the (social) value of information in a quadratic non-cooperative game, and (2) the conditions that ensure the social value of information is non-negative.     

The impact of preventive activities on the economics of production systems: Modeling and application

In this paper, the impact of preventive activities on the economics of production systems has been discussed. A defective production system has been used to evaluate the financial return of a system with and without preventive activity. A mathematical model has been developed to simulate the situation. A practical case in the automotive industry has been used to verify the model. According to this research, it has been found that preventive activities will affect the return of the production system, and the effect depends on the cost of the action that has been taken.     

A definition of information,the arrow of information,and its relationship to life

A new definition of information is proposed that is minimalistic and incorporates a lifetime requirement for conditions, (which we define here) applied to anything that can be considered to be information. The definition explicitly treats a state in thermodynamic equilibrium as an effectively zero information state. The definition includes the absolute requirement of selection for achieving information; the selection criterion being that the information directly or indirectly contributes to its own replication. The definition also explicitly incorporates the Laws of Thermodynamics, the Second Law leading to the requirement for replication. Finally, the definition explains the origin of information and predicts the monotonic increase of information with time. Published 2010 Wiley Periodicals, Inc. Complexity, 2011     

The fuzzy decision problem: An approach to the point estimation problem with fuzzy information

This paper is devoted to the extension of the Bayesian method for the point estimation, when the available information is ‘vague’.In the nonfuzzy case, the parametric estimation can be approached as a particularization in the statistical decision problem. This motivates us to accomplish the mentioned extension by looking at the parametric estimation in the fuzzy case as a special situation in the fuzzy decision problem (defined by Tanaka, Okuda and Asia).In this way, concepts in the fuzzy decision problem are first ‘expressed’ in the estimation terminology. Then, on the basis of these concepts, we shall introduce some notions and state some interesting results. Finally, several illustrative examples will be exposed.     

Quantity of information; comparison between information systems: 2. Fuzzy states

In statistical theory, experiments or probabilistic information systems are supposed to be informative, since they reduce the amount of uncertainty associated with the states of nature. For the case that the available information systems are vague (fuzzy information systems), H. Tanaka, T. Okuda and K. Asai have proven, using the ‘measure of information’ as provided by ‘entropy’, that the fuzzy information systems are informative too.Now, we wish to state and to study a criterion in order to compare fuzzy information systems by the ‘quantity of information of a fuzzy information system’ (defined by Tanaka et al.).In the first paper we considered the situation where we require information about the original state space (non-fuzzy state space).This second paper deals with the situation where we require only information on certain vague states (fuzzy states).     

Quantity of information; Comparison between information systems: 1. Non-fuzzy states

In statistical theory, experiments or probabilistic information systems are supposed to be informative, since they reduce the amount of uncertainty associated with the states of nature. For the case that the available information systems are vague (fuzzy information systems), H. Tanaka, T. Okuda and K. Asai have proven, using the ‘measure of information’ as provided by ‘entropy’, that the fuzzy information systems are informative too.Now, we wish to state and to study a criterion in order to compare fuzzy information systems by the ‘quantity of information of a fuzzy information system’ (defined by Tanaka et al.).In this first paper we consider the situation where we require information about the original state space (non-fuzzy state space).The second paper will deal with the situation where we require only information on certain vague states (fuzzy states).     

Selection of variables in two-group discriminant analysis by error rate and Akaike's information criteria

This paper deals with two criteria for selection of variables for the discriminant analysis in the case of two multivariate normal populations with different means and a common covariance matrix. One is based on the estimated error rate of misclassification. The other uses Akaike's information criterion. The asymptotic distributions and error rate risks of the criteria are obtained. The result will prove that the two criteria are asymptotically equivalent in the sense of their asymptotic distributions and error rate risks being identical.     

Lagrange's early contributions to the theory of first-order partial differential equations

In 1776, J. L. Lagrange gave a definition of the concept of a “complete solution” of a first-order partial differential equation. This definition was entirely different from the one given earlier by Euler. One of the sources for Lagrange's reformulation of this concept can be found in his attempt to explain the occurrence of singular solutions of ordinary differential equations. Another source of the new definition is contained in an earlier treatise of Lagrange [1774] in which he elaborated an approach to first-order partial differential equations briefly indicated by Euler. The method of “variation of constants,” which was fundamental to his argument, suggested to Lagrange the reformulation of the concept of a “complete solution.” In the present paper I shall discuss both sources of the new definition of “completeness.”     

Kato's inequality and the comparison of semigroups

Let A be the generator of a positivity preserving semigroup and let B be another semibounded self-adjoint operator. We give necessary and sufficient conditions in terms of the generators for the inequality $\text{¦ e}{}^{\mathrm{?tB}}\text{u ¦ ? e}{}^{\mathrm{?tA}}\text{¦ u ¦}$ to hold pointwise.     

上下极限视角下的斯托尔茨公式和罗必塔法则

利用上下极限,可对斯托尔茨公式和罗必塔法则进行简单的推广,并提供更为简明的证明.另一方面,本文也对多重极限和累次极限之间的关系给出了一个更好的描述.     

Set choice problems with incomplete information about the preferences of the decision maker

We consider the problem of selecting a predetermined number of objects from a given finite set. It is assumed that the preferences of the decision maker on this set are only partially known. Our solution approach is based on the notions of optimal and non-dominated subsets. The properties of such subsets and the objects they contain are investigated. The implementation of the developed approach is discussed and illustrated by various examples.