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This book collects papers from the Special Issue "Singularly Perturbed Problems: Asymptotic Analysis and Approximate Solution", published in Axioms. These papers cover different aspects of singular perturbation theory and its applications: axiomatic approach in the analytic theory of singular perturbations; asymptotic solution of various types of singularly perturbed integral–differential and integral equations with weakly and rapidly varying kernels of the integral operators; propagation of two-dimensional periodic perturbations in a viscous continuously stratified fluid; asymptotic analysis of the stochastic linear–quadratic optimal control problem with two fast timescales in the dynamics; asymptotic solution of singularly perturbed Cauchy problem for different types of differential equations with "simple" turning points; asymptotic analysis of the complete Euclidean space controllability for different types of singularly perturbed differential systems with time delays; asymptotic solution of singularly perturbed systems in the critical case by the orthogonal projector method; application of the direct scheme method to asymptotic solution of one class of optimal control problems with three-tempo state variables; asymptotic analysis and solution of a cheap control linear quadratic zero-sum differential game; analysis of asymptotic behavior of the solutions for one class of singularly perturbed Neumann boundary value problems .
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We study the optimal design of a disinflation plan by a planner who lacks commitment. Having announced a plan, the Central banker faces a tradeoff between surprise inflation and building reputation, defined as the private sector's belief that the Central bank is committed to the plan. Some plans are harder to sustain: the planner recognizes that paving out future grounds with temptation leads the way for a negative drift of reputation in equilibrium. Plans that successfully create low inflationary expectations balance promises of lower inflation with dynamic incentives that make them more credible. When announcing the disinflation plan, the planner takes into account these anticipated interactions. We find that, even in the zero reputation limit, a gradual disinflation is preferred despite the absence of inflation inertia in the private economy.
Inflation --- Money and Monetary Policy --- Taxation --- Monetary Policy --- Stochastic and Dynamic Games --- Evolutionary Games --- Repeated Games --- Price Level --- Deflation --- Taxation, Subsidies, and Revenue: General --- Macroeconomics --- Monetary economics --- Public finance & taxation --- Inflation targeting --- Tax incentives --- Disinflation --- Prices --- Monetary policy --- United States
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We study the optimal design of a disinflation plan by a planner who lacks commitment. Having announced a plan, the Central banker faces a tradeoff between surprise inflation and building reputation, defined as the private sector's belief that the Central bank is committed to the plan. Some plans are harder to sustain: the planner recognizes that paving out future grounds with temptation leads the way for a negative drift of reputation in equilibrium. Plans that successfully create low inflationary expectations balance promises of lower inflation with dynamic incentives that make them more credible. When announcing the disinflation plan, the planner takes into account these anticipated interactions. We find that, even in the zero reputation limit, a gradual disinflation is preferred despite the absence of inflation inertia in the private economy.
United States --- Inflation --- Money and Monetary Policy --- Taxation --- Monetary Policy --- Stochastic and Dynamic Games --- Evolutionary Games --- Repeated Games --- Price Level --- Deflation --- Taxation, Subsidies, and Revenue: General --- Macroeconomics --- Monetary economics --- Public finance & taxation --- Inflation targeting --- Tax incentives --- Disinflation --- Prices --- Monetary policy
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International macroeconomic policy coordination is generally considered to be made less likely—and less profitable—by the presence of uncertainty about how the economy works. The present paper provides a counter-example, in which increased uncertainty about portfolio preference of investors makes coordination of monetary policy more beneficial. In particular, in the absence of coordination monetary authorities may respond to financial market uncertainty by not fully accommodating demands for increased liquidity, for fear of bringing about exchange rate depreciation. Coordinated monetary expansion would minimize this danger. A theoretical model incorporating an equity market is developed, and the stock market crash of October 1987 is discussed in the light of its implications for monetary policy coordination.
Finance: General --- Foreign Exchange --- Investments: Stocks --- Macroeconomics --- Stochastic and Dynamic Games --- Evolutionary Games --- Repeated Games --- Financial Markets and the Macroeconomy --- Monetary Policy --- Pension Funds --- Non-bank Financial Institutions --- Financial Instruments --- Institutional Investors --- General Financial Markets: General (includes Measurement and Data) --- Price Level --- Inflation --- Deflation --- Macroeconomics: Consumption --- Saving --- Wealth --- Investment & securities --- Finance --- Currency --- Foreign exchange --- Stocks --- Stock markets --- Asset prices --- Exchange rates --- Consumption --- Financial institutions --- Financial markets --- Prices --- National accounts --- Stock exchanges --- Economics --- United States
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This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. The selected contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 13th International Symposium of Dynamic Games and Applications held in Wrocław. The book covers a variety of topics, ranging from theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as environmental management, finance and economics, engineering, guidance and control, and social interaction. The book is thematically organized into five parts: * Theoretical developments in differential and dynamic games; * Pursuit-evasion and guidance games; * Evolutionary games; * Stability and time consistency in cooperative games; * Applications and numerical approaches in environmental and renewable resource management, finance, insurance and economics, supply chains, and telecommunications. Featured throughout are useful tools and valuable resources for researchers, practitioners, and graduate students interested in dynamic games and their applications in applied mathematics, engineering, economics, and management science. Also included in the volume is a special tribute to Arik Melikyan, honoring his memory and the many contributions he made to the field of dynamic games.
Dynamic games. --- Game theory -- Congresses. --- Game theory. --- Differential games --- Stochastic processes --- Business & Economics --- Mathematics --- Economic Theory --- Algebra --- Physical Sciences & Mathematics --- Differential games. --- Stochastic processes. --- Random processes --- Games, Differential --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Game Theory. --- Applications of Mathematics. --- Appl.Mathematics/Computational Methods of Engineering. --- Genetics and Population Dynamics. --- Probabilities --- Game theory --- Genetics --- Mathematical and Computational Engineering. --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Engineering --- Engineering analysis --- Mathematical analysis --- Games, Theory of --- Theory of games --- Mathematical models --- Math --- Science
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Central bank digital currencies (CBDCs) promise many benefits but, if not well designed, they could have undesired consequences, including for monetary policy. Issuing an unremunerated CBDC or a wholesale CBDC does not change the objectives of monetary policy or the operational framework for monetary policy. CBDCs can, however, induce changes in the retail, wholesale and cross border payments that have negative spillover effects on monetary policy, through their effects on money velocity, bank deposit disintermediation, volatility of bank reserves, currency substitution, and capital flows. Countries most vulnerable are those with banking systems dominated by small retail deposits and demand deposits, low levels of digital payments and weak macro fundamentals. Proposed CBDC design features, such as caps on CBDC holdings and unremunerating the CBDC can moderate disintermediation risks, but they are not sufficient. Central banks will need to ensure that unintended macroeconomic risks are comprehensively identified and mitigated.
Macroeconomics --- Economics: General --- Industries: Financial Services --- Money and Monetary Policy --- Banks and Banking --- Islamic Banking and Finance --- Noncooperative Games --- Stochastic and Dynamic Games --- Evolutionary Games --- Repeated Games --- Market Structure and Pricing: General --- Demand for Money --- Monetary Systems --- Standards --- Regimes --- Government and the Monetary System --- Payment Systems --- Monetary Policy --- Central Banks and Their Policies --- Management of Technological Innovation and R&D --- Technological Change: Choices and Consequences --- Diffusion Processes --- Banks --- Depository Institutions --- Micro Finance Institutions --- Mortgages --- Information and Internet Services --- Computer Software --- Other Economic Systems: Public Economics --- Financial Economics --- Monetary Policy, Central Banking, and the Supply of Money and Credit: General --- Economic & financial crises & disasters --- Economics of specific sectors --- Banking --- Distributed ledgers --- Monetary economics --- Technology --- Financial institutions --- Money --- Financial services --- Central Bank digital currencies --- Commercial banks --- Velocity of money --- Islamic banking --- Monetary base --- Currency crises --- Informal sector --- Economics --- Financial services industry --- Technological innovations --- Banks and banking --- Islamic countries --- Money supply --- United States
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Central bank digital currencies (CBDCs) promise many benefits but, if not well designed, they could have undesired consequences, including for monetary policy. Issuing an unremunerated CBDC or a wholesale CBDC does not change the objectives of monetary policy or the operational framework for monetary policy. CBDCs can, however, induce changes in the retail, wholesale and cross border payments that have negative spillover effects on monetary policy, through their effects on money velocity, bank deposit disintermediation, volatility of bank reserves, currency substitution, and capital flows. Countries most vulnerable are those with banking systems dominated by small retail deposits and demand deposits, low levels of digital payments and weak macro fundamentals. Proposed CBDC design features, such as caps on CBDC holdings and unremunerating the CBDC can moderate disintermediation risks, but they are not sufficient. Central banks will need to ensure that unintended macroeconomic risks are comprehensively identified and mitigated.
United States --- Macroeconomics --- Economics: General --- Industries: Financial Services --- Money and Monetary Policy --- Banks and Banking --- Islamic Banking and Finance --- Noncooperative Games --- Stochastic and Dynamic Games --- Evolutionary Games --- Repeated Games --- Market Structure and Pricing: General --- Demand for Money --- Monetary Systems --- Standards --- Regimes --- Government and the Monetary System --- Payment Systems --- Monetary Policy --- Central Banks and Their Policies --- Management of Technological Innovation and R&D --- Technological Change: Choices and Consequences --- Diffusion Processes --- Banks --- Depository Institutions --- Micro Finance Institutions --- Mortgages --- Information and Internet Services --- Computer Software --- Other Economic Systems: Public Economics --- Financial Economics --- Monetary Policy, Central Banking, and the Supply of Money and Credit: General --- Economic & financial crises & disasters --- Economics of specific sectors --- Banking --- Distributed ledgers --- Monetary economics --- Technology --- Financial institutions --- Money --- Financial services --- Central Bank digital currencies --- Commercial banks --- Velocity of money --- Islamic banking --- Monetary base --- Currency crises --- Informal sector --- Economics --- Financial services industry --- Technological innovations --- Banks and banking --- Islamic countries --- Money supply
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The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner.
pursuit --- control functions --- integral constraints --- strategies --- value of the game --- decision-making --- game theory --- project management --- differential games --- cooperative differential games --- Time Consistency --- IDP-core --- IDP dominance --- two-sided platform market --- pricing --- Hotelling’s duopoly on the plane --- Nash equilibrium --- optimal location of platforms --- prescribed duration --- characteristic function --- environmental resource management --- pollution control --- discrete-time games --- cooperation --- the core --- linear transformation --- time consistency --- multistage game --- chance moves --- subgame perfect equilibria --- cooperative trajectory --- imputation distribution procedure --- random time horizon --- time until failure --- discounted equilibrium --- weibull distribution --- chen distribution --- equivalence principle --- cooperative game --- satisfaction criteria --- proportional value --- axiomatization --- cooperative stochastic game --- strong subgame consistency --- core --- dynamic games --- multicriteria games --- Nash bargaining solution --- dynamic stability --- rational behavior conditions --- Shapley-Solidarity value --- coalition structure --- potential --- bidding mechanism
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The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner.
Research & information: general --- Mathematics & science --- pursuit --- control functions --- integral constraints --- strategies --- value of the game --- decision-making --- game theory --- project management --- differential games --- cooperative differential games --- Time Consistency --- IDP-core --- IDP dominance --- two-sided platform market --- pricing --- Hotelling’s duopoly on the plane --- Nash equilibrium --- optimal location of platforms --- prescribed duration --- characteristic function --- environmental resource management --- pollution control --- discrete-time games --- cooperation --- the core --- linear transformation --- time consistency --- multistage game --- chance moves --- subgame perfect equilibria --- cooperative trajectory --- imputation distribution procedure --- random time horizon --- time until failure --- discounted equilibrium --- weibull distribution --- chen distribution --- equivalence principle --- cooperative game --- satisfaction criteria --- proportional value --- axiomatization --- cooperative stochastic game --- strong subgame consistency --- core --- dynamic games --- multicriteria games --- Nash bargaining solution --- dynamic stability --- rational behavior conditions --- Shapley-Solidarity value --- coalition structure --- potential --- bidding mechanism
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This fintech note presents an analysis of the implications of central bank digital currency (CBDC) for monetary policy. In our framework, the implications of CBDC issuance on monetary policy are intermediated by its impact on key parts of the macroeconomic environment. The note also makes a distinction between “level effects”—whereby the introduction of CBDCs could tighten or loosen financial conditions as a shock—and “transmission effects,” whereby CBDCs change the impact of a given monetary policy shock on output, employment, and inflation. In general, the effects of CBDCs on monetary policy transmission are expected to be relatively small in normal times; however, these effects can be more significant in an environment with low interest rates or financial market stress.
Bank deposits --- Banking --- Banks and Banking --- Banks and banking --- Banks and banking, Central --- Banks --- Central Bank digital currencies --- Central bank policy rate --- Central Banks and Their Policies --- Central banks --- Computer Software --- Demand for Money --- Depository Institutions --- Diffusion Processes --- Distributed ledgers --- Economic & financial crises & disasters --- Economic sectors --- Economics of specific sectors --- Economics: General --- Evolutionary Games --- Finance --- Finance: General --- Financial inclusion --- Financial Markets and the Macroeconomy --- Financial markets --- Financial services industry --- Financial services --- Government and the Monetary System --- Industries: Financial Services --- Information and Internet Services --- Interest rates --- Interest Rates: Determination, Term Structure, and Effects --- Macroeconomics --- Management of Technological Innovation and R&D --- Market Structure and Pricing: General --- Micro Finance Institutions --- Monetary Policy --- Monetary Systems --- Mortgages --- Noncooperative Games --- Open market operations --- Payment Systems --- Regimes --- Repeated Games --- Standards --- Stochastic and Dynamic Games --- Technological Change: Choices and Consequences --- Technological innovations --- Technology
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