Note: Bibliography: p. 559-564 , Translation of: Applications des inéquations variationnelles en contrôle stochastique

Note: Includes bibliographies

Note: Bibliography: p. 399-410

Note: Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Preface -- PART 1. Scientific Resources and Data Economy -- 1. Data Production and Sharing: Towards a Universal Right? -- 1.1. The right to knowledge today: between attempts at universalization and "self-regulation" by the GAFA -- 1.1.1. Towards the emergence of a universal right to knowledge subject to divergent economic thinking -- 1.1.2. The recognition of a universal right to knowledge: a "realistic utopia"? -- 1.2. Platform and scientific community rights: the absence of an upfront legal framework -- 1.2.1. A system partly caused by the development of the digital sector -- 1.2.2. The now-fragile law attempting to protect the results of research -- 1.2.3. Intellectual property rights -- 1.2.4. The notion of databases and protection by sui generis law -- 1.2.5. Problems with the legal statute of knowledge -- 1.3. The need to elaborate several types of legislation -- 1.3.1. Platform rights -- 1.3.2. Text and Data Mining: the great new stake -- 1.4. Open Science: an achievable goal? -- 2. Data: a Simple Raw Material? -- 2.1. The new generation of data: management issues arising from ownership rights -- 2.2. How to transform these data into knowledge? -- 2.3. A new knowledge economy is necessary -- 2.3.1. The information war and the stakes of data protection -- 2.4. International scientific publishing: high added-value services and researcher community -- 2.4.1. The open platform as the preferred tool for sharing and exploiting data -- 2.4.2. An undeniable added value in processing data brought about by platforms -- 3. New Knowledge Tools -- 3.1. Sharing and uncertainty -- 3.2. Platform construction -- 3.3. Machine learning -- 3.4. Promising progress to be qualified… -- PART 2. The Knowledge Factory -- 4. Economic Models of Knowledge Sharing -- 4.1. A quick historic overview. , 4.2. Property and/or sharing -- 4.3. An immaterial good capable of fueling the production of material goods -- 4.4. The large stakes of knowledge production -- 4.4.1. Limits of this model: consistency, reliability and indistinction -- 4.4.2. Business models of knowledge sharing -- 4.4.3. Some numbers -- 4.5. Development prospects allowing for new fields of study and more nimbly integrating researchers into the economic chain -- 5. From the Author to the Valorizer -- 5.1. The author and the valorizer: conciliation and efficiency of the interaction -- 5.2. One point on patents -- 5.3. The innovation cycle -- 5.4. The law for a Digital Republic -- 5.5. Scientific openness surpassing ancient legal tools -- 6. Valorization: a Global Geopolitical Stake -- 6.1. A multispeed competition -- 6.1.1. The United States: a country losing its lead -- 6.1.2. French stagnation -- 6.1.3. The expanding Chinese model -- 6.2. International cooperation in the scientific sector -- 6.2.1. A developing European project -- 6.2.2. International organizations -- 7. Focus: the Chinese Patent Strategy -- 7.1. Chinese expansion -- 7.2. An inflation of Chinese patents -- 7.3. Some fallbacks in China nuancing its strategic position -- 7.3.1. A fallback in favor of applied research -- 7.3.2. Territorial withdrawal -- 7.3.3. A long certification process with uncertain ends -- 7.3.4. The procedure for submitting a dispute on a patent -- 7.4. Contestable and contested digital supremacy -- 8. Artificial Intelligence Policies -- 8.1. Policies concerning "strong" AI -- 8.2. Policies concerning "weak" AI -- 8.3. Policies concerning artificial intelligence safety -- 8.4. From practice to ethics: what is AI's legal status? -- 9. New Formulations of Results and New "Markets" -- 9.1. Making universal: establishing common standards of expression -- 9.1.1. Requirement of uniqueness. , 9.1.2. Hierarchy requirement -- 9.2. To adapt: from popularization to simplification -- 9.2.1. Versatility or specialization? -- 9.2.2. Simplifying rather than popularizing -- 9.2.3. Measures following the precautionary principle: archiving and protection -- 9.2.4. Preserving the researcher while optimizing knowledge for the general interest during the digital era -- 9.3. Developing the general state of knowledge with care -- 10. Open Science: a Common Good that Needs to be Valued? -- 10.1. A global challenge that must take the economy into account -- 10.2. A wide variety of public policies respond to this challenge -- 10.2.1. Enterprises and States -- 10.2.2. Valorization as a junction point -- 10.2.3. Basic research: competing with applied research? -- 10.3. The French case and international rankings -- 10.4. The limits of the patent system and publication count -- 10.5. Investment tools aiming to correct these failures -- 10.6. How to measure innovation? -- 10.6.1. The university: the first knowledge production framework recognized by law -- 10.6.2. Research data: a new intangible "place" for producing knowledge -- 10.7. The application of research is not an end in itself -- Conclusion -- Appendices -- Appendix 1: Extract from the CNRS White Paper: "The Work of Science and the Digital Field: Data, Publications, Platforms. A Systematic Analysis of the Law for a Digital Republic" -- Appendix 2: Extract from the CNRS White Paper "Open Science in a Digital Republic: Studies and Proposals for Law Application. Strategic Application Guide" -- Bibliography -- List of Authors -- Index -- EULA.

Note: Intro -- Preface -- Acknowledgments -- Contents -- Chapter 1: Introduction -- Chapter 2: General Presentation of Mean Field Control Problems -- 2.1 Model and Assumptions -- 2.2 Definition of the Problems -- Chapter 3: The Mean Field Games -- 3.1 HJB-FP Approach -- 3.2 Stochastic Maximum Principle -- Chapter 4: The Mean Field Type Control Problems -- 4.1 HJB-FP Approach -- 4.2 Other Approaches -- 4.3 Stochastic Maximum Principle -- 4.4 Time Inconsistency Approach -- Chapter 5: Approximation of Nash Games with a Large Number of Players -- 5.1 Preliminaries -- 5.2 System of PDEs -- 5.3 Independent Trajectories -- 5.4 General Case -- 5.5 Nash Equilibrium Among Local Feedbacks -- Chapter 6: Linear Quadratic Models -- 6.1 Setting of the Model -- 6.2 Solution of the Mean Field Game Problem -- 6.3 Solution of the Mean Field Type Problem -- 6.4 The Mean Variance Problem -- 6.5 Approximate N Player Differential Game -- Chapter 7: Stationary Problems -- 7.1 Preliminaries -- 7.2 Mean Field Game Set-Up -- 7.3 Additional Interpretations -- 7.4 Approximate N Player Nash Equilibrium -- Chapter 8: Different Populations -- 8.1 General Considerations -- 8.2 Multiclass Agents -- 8.3 Major Player -- 8.3.1 General Theory -- 8.3.2 Linear Quadratic Case -- Chapter 9: Nash Differential Games with Mean Field Effect -- 9.1 Description of the Problem -- 9.2 Mathematical Problem -- 9.3 Interpretation -- 9.4 Another Interpretation -- 9.5 Generalization -- 9.6 Approximate Nash Equilibrium for Large Communities -- Chapter 10: Analytic Techniques -- 10.1 General Set-Up -- 10.1.1 Assumptions -- 10.1.2 Weak Formulation -- 10.2 A Priori Estimates for u -- 10.2.1 L∞ Estimate for u -- 10.2.2 L2(W1,2)) Estimate for u -- 10.2.3 Cα Estimate for u -- 10.2.4 Lp(W2,p) Estimate for u -- 10.3 A Priori Estimates for m -- 10.3.1 L2(W1,2) Estimate -- 10.3.2 L∞(L∞) Estimates. , 10.3.3 Further Estimates -- 10.3.4 Statement of the Global A Priori Estimate Result -- 10.4 Existence Result -- References -- Index.

Note: Intro -- Contents -- 1 Introduction -- 2 State Representation of Linear Dynamical Systems -- 2.1 General Description -- 2.1.1 The Model: Internal Representation -- 2.1.2 Fundamental Matrix -- 2.1.3 External Representation -- 2.1.4 Stationary Case -- 2.2 Controllability -- 2.3 Stability -- 2.3.1 Definition -- 2.3.2 Stabilizability -- 2.4 Observability -- 2.4.1 Definition -- 2.4.2 Observers -- 3 Optimal Control of Linear Dynamical Systems -- 3.1 Finite Horizon Problem -- 3.1.1 Solution of the Problem -- 3.1.2 Proof of Theorem -- 3.2 Infinite Horizon Problem -- 3.3 Positivity -- 3.3.1 Positive Real Lemma -- 3.3.2 Characterization of P -- 4 Estimation Theory -- 4.1 Deterministic Approach -- 4.2 Bayesian Approach -- 4.2.1 Definition -- 4.2.2 Examples -- 4.3 Good Estimators -- 4.3.1 Properties -- 4.3.2 The Cramér-Rao Inequality -- 4.4 Minimum Mean Square Estimator -- 4.4.1 Definition -- 4.4.2 Properties -- 4.4.3 MMSE for Gaussian Variables -- 4.5 Minimum Variance Linear Estimator -- 4.5.1 Definition -- 4.5.2 Necessary and Sufficient Condition -- 4.5.3 Least Squares Estimator -- 4.5.4 A Particular Structure -- 4.6 The Maximum Likelihood Method -- 4.6.1 Definition -- 4.6.2 Properties -- 4.6.3 Maximum Posterior Probability Estimators -- 4.7 Dynamic Models -- 4.7.1 Fixed Parameter -- 4.7.2 Recursive Formulas -- 4.7.3 Dual Formulation -- 4.7.4 The Gaussian Case -- 4.7.5 The Kalman Filter in Discrete Time -- 4.8 Appendix -- 4.8.1 Preliminaries -- 4.8.2 Consistency -- 4.8.3 Asymptotic Normality -- 5 Further Techniques of Estimation -- 5.1 Generalized Linear Models -- 5.2 Examples -- 5.2.1 The Gaussian Distribution -- 5.2.2 The Exponential Distribution -- 5.2.3 The Poisson Distribution -- 5.2.4 The Binomial Distribution -- 5.2.5 The Gamma Distribution -- 5.2.6 The Weibull Distribution -- 5.2.7 Nonlinear Gaussian Model -- 5.2.8 Canonical Links. , 5.3 MLE for Generalized Linear Models -- 5.3.1 Statement of the Problem and Notation -- 5.3.2 Examples -- 5.3.3 Consistency -- 5.3.4 Further Consistency Estimates -- 5.3.5 Asymptotic Normality -- 5.4 The Vector Case -- 5.4.1 Notation and Preliminaries -- 5.4.2 MLE Estimate -- 5.4.3 The Gaussian Case -- 5.4.4 Recursivity -- 5.4.5 Examples -- 5.4.5.1 The Binomial Distribution -- 5.4.5.2 The Poisson Distribution -- 5.4.5.3 The Gamma Distribution -- 5.5 Dynamic Models -- 5.5.1 General Bayesian Approach -- 5.5.1.1 Preliminaries -- 5.5.1.2 Recurrence Formulas -- 5.5.2 Dynamic GLM -- 5.5.2.1 Conditional Probability -- 5.5.2.2 The First Two Moments -- 5.5.3 Applications -- 5.5.3.1 Kalman Filter -- 5.5.3.2 The Poisson Distribution -- 5.5.3.3 The Kalman Filter Revisited -- 5.5.4 First Two Moments Revisited -- 5.5.4.1 General Ideas -- 5.5.4.2 Model and Approximation -- 5.5.4.3 Further Approximation -- 5.5.5 Example of a Beta Model -- 5.6 Seasonal Factors -- 5.6.1 Setting of the Problem -- 5.6.2 Moving Averages -- 5.6.3 Exponential Smoothing -- 5.6.4 Estimation of the Trend -- 5.6.5 Holt-Winters Formulas with Seasonality -- 6 Complements on Probability Theory -- 6.1 Probability Concepts -- 6.1.1 Review of Basic Probability Concepts -- 6.1.2 Conditional Expectation -- 6.2 Stochastic Processes -- 6.2.1 General Concepts -- 6.2.2 Wiener Process -- 6.3 Stochastic Calculus -- 6.3.1 Stochastic Integrals -- 6.3.2 Stochastic Differential -- 6.4 Stochastic Differential Equations -- 6.5 Girsanov's Theorem -- 7 Filtering Theory in Continuous Time -- 7.1 Kalman Filters in Continuous Time -- 7.1.1 Statement of the Problem -- 7.1.2 The Innovation Process -- 7.1.3 Proof of Theorem 7.1 -- 7.2 Complements -- 7.3 Control Problems Related to Filtering Theory -- 7.3.1 Minimum-Variance Linear Estimator -- 7.3.2 Least Squares Estimator. , 8 Stochastic Control of Linear Dynamical Systems with Full Information -- 8.1 The Basic Problem -- 8.2 A More Elaborate Model with Control on the Diffusion Term -- 8.3 Exponential-of-Integral Payoff -- 8.3.1 Setting of the Problem -- 8.3.2 The Formal Method -- 8.3.3 Solution -- 9 Stochastic Control of Linear Dynamical Systems with Partial Information -- 9.1 General Discussion -- 9.2 A Class of Admissible Controls -- 9.3 The Separation Principle -- 9.4 Exponential-of-Integral Payoff and Partial Information -- 9.4.1 Setting of the Problem -- 9.4.2 Statement of the Solution -- 9.4.3 Proof of Proposition 9.2 -- 10 Deterministic Optimal Control -- 10.1 Pontryagin's Maximum Principle -- 10.1.1 Setting of the Problem -- 10.1.2 Necessary Condition of Optimality -- 10.1.3 Gâteaux Differential -- 10.1.4 Example -- 10.2 Dynamic Programming -- 10.2.1 Invariant Embedding and Optimality Principle -- 10.2.2 HJB Equation -- 10.2.3 Verification Principle -- Regularity -- 10.3 Links Between the Maximum Principle and Dynamic Programming -- 10.4 No Smoothness Case and Viscosity Approach -- 10.4.1 Characterization That Does Not Require Derivatives -- 10.4.2 Viscosity Solutions -- 10.4.2.1 Differentials -- 10.4.2.2 Viscosity Solution -- 10.4.2.3 Maximum Principle -- 11 Stochastic Optimal Control -- 11.1 Stochastic Maximum Principle -- 11.1.1 Setting of the Problem -- 11.1.2 Gâteaux Differential -- 11.1.3 Equations for p and r -- 11.2 Stochastic Dynamic Programming -- 11.2.1 Preliminaries -- Optimality Principle -- 11.2.2 HJB Equation -- 11.3 Weak Solution of Stochastic Differential Equations -- 11.3.1 The Concept -- 11.3.2 Generalization of Itô's Formula -- 11.3.3 Interpretation of Solutions of Linear PDEs -- 11.4 Weak Formulation of Stochastic Control -- 11.4.1 Setting of the Problem -- 11.4.2 The HJB Equation -- 11.4.3 Stochastic Control. , 11.5 Connection Between FBSDE and Partial Differential Equations -- 11.6 Links Between Dynamic Programming and the Stochastic Maximum Principle -- 11.7 Calculus of Variations Approach -- 11.7.1 Markov Properties of Diffusions -- 11.7.2 Feedback Control of Probability Densities -- 11.8 Viscosity Theory -- 11.8.1 Second-Order Sub- and Superdifferentials -- 11.8.2 The Crandall-Ishii Lemma -- 11.8.3 Viscosity Solutions -- 11.8.4 Existence -- Perron's Method -- 11.8.5 Stochastic Perron's Method -- 12 Additional Results for BSDE -- 12.1 Solutions of Parabolic PDEs -- 12.1.1 General Comments -- 12.1.2 General Result -- 12.1.3 Growth Discussion -- 12.1.4 Sufficient Condition -- 12.1.5 Main Result -- 12.2 Methodology -- 12.2.1 Continuous Hamiltonian -- 12.2.2 Proof of Theorem 12.1 -- 12.2.3 Formal Proof of Theorem 12.2 -- 12.3 Solutions of BSDEs -- 12.3.1 Statement of the Problem -- 12.3.2 Integrability Condition and Existence -- 12.3.3 Methodology -- 12.3.4 Quadratic Growth Case -- 12.3.5 Proof of Uniqueness -- 13 Stochastic Control Problems in Finance -- 13.1 General Description -- 13.1.1 Financial Markets -- 13.1.2 Optimal Consumption and Investment Problem -- 13.2 Dynamic Equation Approach -- 13.2.1 HJB Equation -- 13.2.2 Solution of the HJB Equation -- 13.3 Solution of the Consumer-Investor Problem -- 13.4 Entrepreneur Decision-Making -- 13.4.1 The Model -- 13.4.2 Dynamic Programming -- 13.4.3 Choice of Initial Conditions -- 13.4.4 Solution of the Bellman Equation -- 13.4.5 Solution of the Stochastic Control Problem -- 13.5 The Martingale Method -- 13.5.1 The Case α=0,δ=0 -- 13.6 Optimal Loan -- 13.7 Duality -- 13.7.1 Consumer-Investor Problem -- 13.7.2 Entrepreneur Problem -- 13.8 Optimal Retirement -- 13.8.1 Setting of the Problem -- 13.8.2 Variational Inequality -- 13.8.3 Solution of the Linear Problem -- 13.8.4 Equation for. , 13.8.5 Solution of the Optimal Retirement Problem -- 14 Stochastic Control for Non-Markov Processes -- 14.1 Statement of the Problem -- 14.2 Backward Stochastic Partial Differential Equations -- 14.3 Nonlinear BSPDE -- 14.4 The Case of Two Noises -- 14.5 The Linear-Quadratic Case -- 15 Principal Agent Control Problems -- 15.1 Risk Sharing -- 15.1.1 Setting of the Model -- 15.1.2 Reduction to the Entrepreneur's Problem -- 15.1.3 Solution -- 15.1.4 Example -- 15.2 Implementing Contracts -- 15.2.1 Decentralized Solution -- 15.2.2 Implementing the Team Solution -- 15.2.3 Generalizations -- 15.2.3.1 Effort of the Agent -- 15.2.3.2 Nonlinear Volatility Selection with Exponential Utilities -- 15.3 General Approach -- 15.3.1 Description of the Problem -- 15.3.2 The Agent Problem -- 15.3.3 The Principal Problem -- 15.3.4 Generalization -- 15.3.5 Study of Problems (15.3.28), (15.3.29), (15.3.30), and (15.3.23) -- 15.4 Examples and Applications -- 15.4.1 Exponential Utilities and Lump-Sum Payments -- 15.4.2 General Utilities, Quadratic Cost, and Lump-Sum Payments -- 15.4.3 Risk-Neutral Principal and Log-Utility Agent -- 15.4.4 Moral Hazard with Unobservable Effort -- 15.5 Contracting Under Hidden Agent Type -- 15.5.1 The Problem -- 15.5.2 Preliminaries -- 15.5.3 The Principal's Problem -- 15.5.4 Examples -- 15.5.5 Controlling Volatility -- 16 Differential Games -- 16.1 Open-Loop Deterministic Nash Equilibrium -- 16.1.1 Description of the Problem -- 16.1.2 Maximum Principle -- 16.1.3 Example -- 16.2 Closed-Loop Deterministic Nash Equilibrium -- 16.2.1 Setting of the Problem -- 16.2.2 Dynamic Programming -- 16.2.3 Example -- 16.3 Deterministic Linear-Quadratic Games -- 16.3.1 Open-Loop Nash Equilibrium -- 16.3.2 Closed-Loop Nash Equilibrium -- 16.3.3 Two-Person Zero-Sum Differential Game: Open-Loop Controls. , 16.3.4 Two-Person Zero-Sum Differential Game: Closed-Loop Controls.

Note: Literaturangaben