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In a world dominated by uncertainty, modeling and understanding the optimal behavior of agents is of the utmost importance. Many problems in economics, finance, and actuarial science naturally require decision makers to undertake choices in stochastic environments. Examples include optimal individual consumption and retirement choices, optimal management of portfolios and risk, hedging, optimal timing issues in pricing American options, and investment decisions. Stochastic control theory provides the methods and results to tackle all such problems. This book is a collection of the papers published in the Special Issue “Applications of Stochastic Optimal Control to Economics and Finance”, which appeared in the open access journal Risks in 2019. It contains seven peer-reviewed papers dealing with stochastic control models motivated by important questions in economics and finance. Each model is rigorously mathematically funded and treated, and the numerical methods are employed to derive the optimal solution. The topics of the book’s chapters range from optimal public debt management to optimal reinsurance, real options in energy markets, and optimal portfolio choice in partial and complete information settings. From a mathematical point of view, techniques and arguments of dynamic programming theory, filtering theory, optimal stopping, one-dimensional diffusions and multi-dimensional jump processes are used.

Economics, finance, business & management --- debt crisis --- government debt management --- optimal government debt ceiling --- government debt ratio --- stochastic control --- decision analysis --- risk management --- Bayesian learning --- Markowitz problem --- optimal portfolio --- portfolio selection --- Markov additive processes --- Markov regime switching market --- Markovian jump securities --- asymptotic arbitrage --- complete market --- multiple optimal stopping --- general diffusion --- real option analysis --- energy imbalance market --- optimal reinsurance --- excess-of-loss reinsurance --- Hamilton-Jacobi-Bellman equation --- stochastic factor model --- American options --- least square method --- derivatives pricing --- binomial tree --- stochastic interest rates --- quadrinomial tree --- insurance --- unemployment --- optimal stopping --- geometric Brownian motion --- martingale --- free boundary problem --- American call option --- utility

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In a world dominated by uncertainty, modeling and understanding the optimal behavior of agents is of the utmost importance. Many problems in economics, finance, and actuarial science naturally require decision makers to undertake choices in stochastic environments. Examples include optimal individual consumption and retirement choices, optimal management of portfolios and risk, hedging, optimal timing issues in pricing American options, and investment decisions. Stochastic control theory provides the methods and results to tackle all such problems. This book is a collection of the papers published in the Special Issue “Applications of Stochastic Optimal Control to Economics and Finance”, which appeared in the open access journal Risks in 2019. It contains seven peer-reviewed papers dealing with stochastic control models motivated by important questions in economics and finance. Each model is rigorously mathematically funded and treated, and the numerical methods are employed to derive the optimal solution. The topics of the book’s chapters range from optimal public debt management to optimal reinsurance, real options in energy markets, and optimal portfolio choice in partial and complete information settings. From a mathematical point of view, techniques and arguments of dynamic programming theory, filtering theory, optimal stopping, one-dimensional diffusions and multi-dimensional jump processes are used.

debt crisis --- government debt management --- optimal government debt ceiling --- government debt ratio --- stochastic control --- decision analysis --- risk management --- Bayesian learning --- Markowitz problem --- optimal portfolio --- portfolio selection --- Markov additive processes --- Markov regime switching market --- Markovian jump securities --- asymptotic arbitrage --- complete market --- multiple optimal stopping --- general diffusion --- real option analysis --- energy imbalance market --- optimal reinsurance --- excess-of-loss reinsurance --- Hamilton-Jacobi-Bellman equation --- stochastic factor model --- American options --- least square method --- derivatives pricing --- binomial tree --- stochastic interest rates --- quadrinomial tree --- insurance --- unemployment --- optimal stopping --- geometric Brownian motion --- martingale --- free boundary problem --- American call option --- utility

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• Reference Manager
• EndNote
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This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws-PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs-mixed type, free boundaries, and corner singularities-that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.

Shock waves --- Von Neumann algebras. --- MATHEMATICS / Differential Equations / Partial. --- Algebras, Von Neumann --- Algebras, W --- Neumann algebras --- Rings of operators --- W*-algebras --- C*-algebras --- Hilbert space --- Shock (Mechanics) --- Waves --- Diffraction --- Diffraction. --- Mathematics. --- A priori estimate. --- Accuracy and precision. --- Algorithm. --- Andrew Majda. --- Attractor. --- Banach space. --- Bernhard Riemann. --- Big O notation. --- Boundary value problem. --- Bounded set (topological vector space). --- C0. --- Calculation. --- Cauchy problem. --- Coefficient. --- Computation. --- Computational fluid dynamics. --- Conjecture. --- Conservation law. --- Continuum mechanics. --- Convex function. --- Degeneracy (mathematics). --- Demetrios Christodoulou. --- Derivative. --- Dimension. --- Directional derivative. --- Dirichlet boundary condition. --- Dirichlet problem. --- Dissipation. --- Ellipse. --- Elliptic curve. --- Elliptic partial differential equation. --- Embedding problem. --- Equation solving. --- Equation. --- Estimation. --- Euler equations (fluid dynamics). --- Existential quantification. --- Fixed point (mathematics). --- Flow network. --- Fluid dynamics. --- Fluid mechanics. --- Free boundary problem. --- Function (mathematics). --- Function space. --- Fundamental class. --- Fundamental solution. --- Fundamental theorem. --- Hyperbolic partial differential equation. --- Initial value problem. --- Iteration. --- Laplace's equation. --- Linear equation. --- Linear programming. --- Linear space (geometry). --- Mach reflection. --- Mathematical analysis. --- Mathematical optimization. --- Mathematical physics. --- Mathematical problem. --- Mathematical proof. --- Mathematical theory. --- Mathematician. --- Melting. --- Monotonic function. --- Neumann boundary condition. --- Nonlinear system. --- Numerical analysis. --- Parameter space. --- Parameter. --- Partial derivative. --- Partial differential equation. --- Phase boundary. --- Phase transition. --- Potential flow. --- Pressure gradient. --- Quadratic function. --- Regularity theorem. --- Riemann problem. --- Scientific notation. --- Self-similarity. --- Special case. --- Specular reflection. --- Stefan problem. --- Structural stability. --- Subspace topology. --- Symmetrization. --- Theorem. --- Theory. --- Truncation error (numerical integration). --- Two-dimensional space. --- Unification (computer science). --- Variable (mathematics). --- Velocity potential. --- Vortex sheet. --- Vorticity. --- Wave equation. --- Weak convergence (Hilbert space). --- Weak solution.