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The purpose of this paper is to research stochastic dynamic investment games with stochastic interest rate model in continuous time between two investors. The market interest rate has the dynamics of Duffie‐Kan interest rate.

Recently, there has been an increasing interest in financial market models whose key parameters, such as the bank interest rate, stocks appreciation rates, and volatility rates, are modulated by stochastic interest rate. This paper uses the Duffie‐Kan stochastic interest rate model to develop stochastic differential portfolio games. By the HJB optimality equation, a general result in optimal control for a stochastic differential game with a general utility payoff function is obtained.

Derive a general result in optimal control for a stochastic differential game with a general utility payoff function. The explicit optimal strategies and value of the games are obtained for the constant relative risk aversion utility games of fixed duration.

Accessibility and availability of stochastic interest rate data are the main limitations, which apply.

The results obtained in this paper could be used as a guide to actual portfolio games.

This paper presents a new approach for the optimal portfolio model under compound jump processes. The paper is aimed at actual portfolio games.

Presents the scientific methodology from the enlarged cybernetical perspective that recognizes the anisotropy of time, the probabilistic character of natural laws, and the entry that the incomplete determinism in Nature opens to the occurrence of innovation, growth, organization, teleology communication, control, contest and freedom. The new tier to the methodological edifice that cybernetics provides stands on the earlier tiers, which go back to the Ionians (c. 500 BC). However, the new insights reveal flaws in the earlier tiers, and their removal strengthens the entire edifice. The new concepts of teleological activity and contest allow the clear demarcation of the military sciences as those whose subject matter is teleological activity involving contest. The paramount question “what ought to be done”, outside the empirical realm, is embraced by the scientific methodology. It also embraces the cognitive sciences that ask how the human mind is able to discover, and how the sequence of discoveries might converge to a true description of reality.

A study is made of the payoff matrix which is made up of grey interval number because of asymmetry information, player's finite knowledge and bounded rationality and all sorts of stochastic and non‐stochastic factors.

On the base of concept of equipollent, superior and inferior potential degree, the paper designs determinant rules of interval grey number potential relations, opens out player's decision‐making laws in the conditions of finite knowledge and logos. And it designs the grey game decision‐making rules which player choices maximum potential degree of grey game value (the most favorableness situation) under the cases of that there are all likely to be minimum potential degree of grey game value (the most disadvantage situation), which is a reliable way for both sides to accept.

The paper recognizes and defines overrated and underrated risk of potential optimal pure strategy in the grey game, designs arithmetic for determining player's overrated and underrated risk under the situation of potential optimal pure strategy.

The presents system meets the requirement of judging pure strategy solutions in the grey potential situation.

This paper builds up the system of judgment for grey potential.

This paper investigates how macroeconomic policy and planning of large‐scale dynamic systems are approached from the cybernetic principle, as can be viewed in the interplay of information, decision and control. Some speculations about directions in large‐scale policy and planning methods are offered.

The dynamic measure of risk problem in a incomplete market is discussed when stock appreciation rates are uncertain. Meanwhile, a related stochastic game problem is studied. The value of a stochastic optimal control is regarded as a reasonable measure of the risk. The form of the optimal objective is obtained by employing the tools of BSDE theory.

The purpose of this paper is to focus on resource allocation and information disclosure policy for defending multiple targets against intentional attacks. The intentional attacks, like terrorism events, probably cause great losses and fatalities. Attackers and defenders usually make decisions based on incomplete information. Adaptive attacking and defending strategies are considered, to study how both sides make more effective decisions according to previous fights.

A stochastic game‐theoretic approach is proposed for modeling attacker‐defender conflicts. Attackers and defenders are supposed both to be strategic decision makers and partially aware of adversary's information. Adaptive strategies are compared with different inflexible strategies in a fortification‐patrol problem, where the fortification affects the security vulnerability of targets and the patrol indicates the defensive signal.

The result shows that the intentional risk would be elevated by adaptive attack strategies. An inflexible defending strategy probably fails when facing uncertainties of adversary. It is shown that the optimal response of defenders is to adjust defending strategies by learning from previous games and assessing behaviors of adversaries to minimize the expected loss.

This paper explores how adaptive strategies affect attacker‐defender conflicts. The key issue is defense allocation and information disclosure policy for mitigation of intentional threats. Attackers and defenders can adjust their strategies by learning from previous fights, and the strategic adjustment of both sides may be asynchronous.

The purpose of this paper is to recuperate Heinz von Foerster’s “Quantum Mechanical Theory of Memory” from Cybernetics: Circular, Causal, and Feedback Mechanisms in Biological and Social Systems and John von Neumann’s The Computer and the Brain for present-day, and future, applications in biophysics, theories of information and cognition, and quantum theories; the main objective is to ground cybernetic theory for a critical evaluation of the historical evolution of the Monte Carlo method, with potential for application to quantum computing.

Close-reading of selected texts, historiography, and case studies in current developments in the Monte Carlo method of high-energy particle physics (HEP) for developing a platform for bridging the apparently incommensurable differences between the physical-mathematical and the biological sciences.

First, usefulness of the cybernetic approach for historicizing the Monte Carlo method in relation to digital computing and quantum physics. Second, development of an inter/trans-disciplinary approach to the hard sciences through a critical re-evaluation of the historical texts of von Foerster and von Neumann for application to developments in quantum theory, biophysics, and computing.

This work is largely theoretical and uses dialectical thought experiments to engage between sciences operating across different ontological scales.

Consideration of developments of quantum computing and how that would change one’s perception of information, data, and the way in which analysis is currently performed with big data.

This is the first time that von Neumann and von Foerster have been contrasted and compared in relation to their epistemic compatibility, historical importance, and relevance for producing a creative approach to current scientific epistemology. This paper hopes to change how the authors view trans-disciplinary/inter-disciplinary practices in the sciences and produce new vistas of thought in the history and philosophy of science.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

It will be shown that the hypothesis of universal determinism fits poorly with the empirical realities of human life, and that no age of science (after 500BC) has embraced it. After tracing the history of universal determinism, we shall show how in the mid‐nineteenth century arose the idea of a stochastic cosmos, in which the laws of nature are probabilistic, and in which “possibilities”, in accord with natural law, are in excess of actualities.