A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where ...A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.展开更多
Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet fo...Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet form on the abstract metric measure space. As an application we obtain lower estimates for heat kernels on some Riemannian manifolds.展开更多
In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be descr...In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes (AFBSDEDLs), we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs' preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.展开更多
This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived vi...This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.展开更多
Optimal glucose feed strategy for glycerol fed-batch fermentation was investigated by Pontryagin’s maximum principle to maximize the final glycerol yield. The problem was solved by a nonsingular control approach by s...Optimal glucose feed strategy for glycerol fed-batch fermentation was investigated by Pontryagin’s maximum principle to maximize the final glycerol yield. The problem was solved by a nonsingular control approach by selecting the culture volume as the control variable, then the general optimal feed profile was numerically determined.展开更多
A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary an...A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.展开更多
This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables...This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.展开更多
In this note we announce the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi’s iteration.In particular,the existence of weak solutions for possibly degenerate s...In this note we announce the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi’s iteration.In particular,the existence of weak solutions for possibly degenerate stochastic differential equations with singular diffusion coefficients is obtained.展开更多
The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in pa...The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in parallel” to the tradition-al ones, such as those based, for example, on the hypotheses of “Dark Matter” and “Dark Energy”, or better as a “com-possible” perspective, because it is not understood as being “exclusive”. In fact, it is an approach that, when con-firmed by experimental results, always keeps its validity from an “operative” point of view. This is because, in analogy to the traditional perspectives, on the basis of Popper’s Falsification Principle the corresponding “Generative” Logic on which it is based has not the property of the perfect induction. The basic difference then only consists in the fact that the Evolution of the Universe is now modeled by considering the Universe as a Self-Organizing System, which is thus analyzed in the light of the Maximum Ordinality Principle.展开更多
In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solu...In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.展开更多
This study advances the G-stochastic maximum principle(G-SMP)from a risk-neutral framework to a risk-sensitive one.A salient feature of this advancement is its applicability to systems governed by stochastic different...This study advances the G-stochastic maximum principle(G-SMP)from a risk-neutral framework to a risk-sensitive one.A salient feature of this advancement is its applicability to systems governed by stochastic differential equations under G-Brownian motion(G-SDEs),where the control variable may influence all terms.We aim to generalize our findings from a risk-neutral context to a risk-sensitive performance cost.Initially,we introduced an auxiliary process to address risk-sensitive performance costs within the G-expectation framework.Subsequently,we established and validated the correlation between the G-expected exponential utility and the G-quadratic backward stochastic differential equation.Furthermore,we simplified the G-adjoint process from a dual-component structure to a singular component.Moreover,we explained the necessary optimality conditions for this model by considering a convex set of admissible controls.To describe the main findings,we present two examples:the first addresses the linear-quadratic problem and the second examines a Merton-type problem characterized by power utility.展开更多
The present paper aims at showing the possible adoption in Psychiatry of a general methodology finalized to prescribe the most appropriate Therapy based on the knowledge of its correlative effects in advance, instead ...The present paper aims at showing the possible adoption in Psychiatry of a general methodology finalized to prescribe the most appropriate Therapy based on the knowledge of its correlative effects in advance, instead of recognizing them ex post. The specific case here considered is the “bipolar disorder”, in which the adoption of three different drugs is the most common practice, although with a possible differentiation between the prescription in the morning and in the evening, respectively. Thus, the proposed methodology will consider the Ordinal Interactions between the various drugs by evaluating their combined effects, which will result as being not a simple additive “sum”, because they are evaluated on the basis of the Maximum Ordinality Principle (MOP) and, in addition, in Adherence to the Explicit Solution to the “Three-Body Problem”. In this way the Methodology here proposed is able to suggest how to account for the synergistic effects of the various drugs, especially when the latter are characterized by different concentrations and, at the same time, by generally different half-lives respectively.展开更多
This paper presents the Solution to the “Three-body Problem” in the Light of the Maximum Ordinality Principle. In the first part, however, it starts with the Solution to the Solar System, made up of “11 Bodies”. T...This paper presents the Solution to the “Three-body Problem” in the Light of the Maximum Ordinality Principle. In the first part, however, it starts with the Solution to the Solar System, made up of “11 Bodies”. This is because, in such a context, the “Three-body Problem” can be analyzed in its all descriptive possibilities. Nonetheless, the paper also presents the Solution to the “Three-body Problem” with reference to Systems totally independent from the Solar System, such as, for example, the “Triple Stars” and the “Triple Galaxies”. In this way, the paper offers a sufficiently complete framework concerning the Solution to the “Three-body Problem”, always in the Light of the Maximum Ordinality Principle, described in detail in Appendix A.展开更多
The main objective of this paper is to demonstrate that the internal processes of Self-Organizing Systems represent a unique and singular process, characterized by their specific generativity. This process can be mode...The main objective of this paper is to demonstrate that the internal processes of Self-Organizing Systems represent a unique and singular process, characterized by their specific generativity. This process can be modeled using the Maximum Ordinality Principle and its associated formal language, known as the “Incipient” Differential Calculus (IDC).展开更多
In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for th...In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.展开更多
It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes? To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which ...It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes? To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.展开更多
In this paper,we study the recursive stochastic optimal control problems.The control domain does not need to be convex,and the generator of the backward stochastic differential equation can contain z.We obtain the var...In this paper,we study the recursive stochastic optimal control problems.The control domain does not need to be convex,and the generator of the backward stochastic differential equation can contain z.We obtain the variational equations for backward stochastic differential equations,and then obtain the maximum principle which solves completely Peng’s open problem.展开更多
We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the ...We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.展开更多
The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete mode...The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete model is one of the key requirements.It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular meshes in 2D.In this paper we consider how to enforce discrete maximum principle for linear finite element solutions for the linear second-order self-adjoint elliptic equation.First approach is based on repair technique,which is a posteriori correction of the discrete solution.Second method is based on constrained optimization.Numerical tests that include anisotropic cases demonstrate how our method works for problems for which the standard finite element methods produce numerical solutions that violate the discrete maximum principle.展开更多
基金supported by the National Basic Research Program of China (973 Program, 2007CB814904)the National Natural Science Foundations of China (10921101)+2 种基金Shandong Province (2008BS01024, ZR2010AQ004)the Science Funds for Distinguished Young Scholars of Shandong Province (JQ200801)Shandong University (2009JQ004),the Independent Innovation Foundations of Shandong University (IIFSDU,2009TS036, 2010TS060)
文摘A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.
文摘Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet form on the abstract metric measure space. As an application we obtain lower estimates for heat kernels on some Riemannian manifolds.
基金Supported by the National Natural Science Foundation(11221061 and 61174092)111 project(B12023),the National Science Fund for Distinguished Young Scholars of China(11125102)Youth Foundation of QiLu Normal Institute(2012L1010)
文摘In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes (AFBSDEDLs), we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs' preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.
文摘This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.
基金From National Ninth Five Years Project (NO. 96-03-03-03A).
文摘Optimal glucose feed strategy for glycerol fed-batch fermentation was investigated by Pontryagin’s maximum principle to maximize the final glycerol yield. The problem was solved by a nonsingular control approach by selecting the culture volume as the control variable, then the general optimal feed profile was numerically determined.
基金supported by the Doctoral foundation of University of Jinan(XBS1213)the National Natural Science Foundation of China(11101242)
文摘A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.
基金supported by the National Natural Science Foundation of China(11701214)Shandong Provincial Natural Science Foundation,China(ZR2019MA045).
文摘This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.
基金The China Scholarship Council,the National Basic Research Program(2009CB219301) of China(973) in partthe National Public Benefit Scientific Research Foundation(201011078) of China+2 种基金the National Innovation Research Project for Exploration and Development of Oil Shale(OSP-02 and OSR-02)the NSF(41304087,11071026,61133011,61170092,60973088,61202308,11001100,11171131 and 11026043) of Chinathe Basic Research Foundation of Jilin University in 2012
文摘In this paper, we have studied the necessary maximum principle of stochastic optimal control problem with delay and jump diffusion.
基金National Natural Science Foundation of China(11731009).
文摘In this note we announce the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi’s iteration.In particular,the existence of weak solutions for possibly degenerate stochastic differential equations with singular diffusion coefficients is obtained.
文摘The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in parallel” to the tradition-al ones, such as those based, for example, on the hypotheses of “Dark Matter” and “Dark Energy”, or better as a “com-possible” perspective, because it is not understood as being “exclusive”. In fact, it is an approach that, when con-firmed by experimental results, always keeps its validity from an “operative” point of view. This is because, in analogy to the traditional perspectives, on the basis of Popper’s Falsification Principle the corresponding “Generative” Logic on which it is based has not the property of the perfect induction. The basic difference then only consists in the fact that the Evolution of the Universe is now modeled by considering the Universe as a Self-Organizing System, which is thus analyzed in the light of the Maximum Ordinality Principle.
基金National Natural Science Foundation of China(11971069,12071045)Foundation of CAEP(CX20210042)Science Challenge Project(No.TZ2016002).
文摘In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.
基金supported by PRFU project N(Grant No.C00L03UN070120220004).
文摘This study advances the G-stochastic maximum principle(G-SMP)from a risk-neutral framework to a risk-sensitive one.A salient feature of this advancement is its applicability to systems governed by stochastic differential equations under G-Brownian motion(G-SDEs),where the control variable may influence all terms.We aim to generalize our findings from a risk-neutral context to a risk-sensitive performance cost.Initially,we introduced an auxiliary process to address risk-sensitive performance costs within the G-expectation framework.Subsequently,we established and validated the correlation between the G-expected exponential utility and the G-quadratic backward stochastic differential equation.Furthermore,we simplified the G-adjoint process from a dual-component structure to a singular component.Moreover,we explained the necessary optimality conditions for this model by considering a convex set of admissible controls.To describe the main findings,we present two examples:the first addresses the linear-quadratic problem and the second examines a Merton-type problem characterized by power utility.
文摘The present paper aims at showing the possible adoption in Psychiatry of a general methodology finalized to prescribe the most appropriate Therapy based on the knowledge of its correlative effects in advance, instead of recognizing them ex post. The specific case here considered is the “bipolar disorder”, in which the adoption of three different drugs is the most common practice, although with a possible differentiation between the prescription in the morning and in the evening, respectively. Thus, the proposed methodology will consider the Ordinal Interactions between the various drugs by evaluating their combined effects, which will result as being not a simple additive “sum”, because they are evaluated on the basis of the Maximum Ordinality Principle (MOP) and, in addition, in Adherence to the Explicit Solution to the “Three-Body Problem”. In this way the Methodology here proposed is able to suggest how to account for the synergistic effects of the various drugs, especially when the latter are characterized by different concentrations and, at the same time, by generally different half-lives respectively.
文摘This paper presents the Solution to the “Three-body Problem” in the Light of the Maximum Ordinality Principle. In the first part, however, it starts with the Solution to the Solar System, made up of “11 Bodies”. This is because, in such a context, the “Three-body Problem” can be analyzed in its all descriptive possibilities. Nonetheless, the paper also presents the Solution to the “Three-body Problem” with reference to Systems totally independent from the Solar System, such as, for example, the “Triple Stars” and the “Triple Galaxies”. In this way, the paper offers a sufficiently complete framework concerning the Solution to the “Three-body Problem”, always in the Light of the Maximum Ordinality Principle, described in detail in Appendix A.
文摘The main objective of this paper is to demonstrate that the internal processes of Self-Organizing Systems represent a unique and singular process, characterized by their specific generativity. This process can be modeled using the Maximum Ordinality Principle and its associated formal language, known as the “Incipient” Differential Calculus (IDC).
基金The first author was supported by Hungarian National Research Fund OTKA No.K67819the second author was partially supported by Hungarian National Research Fund OTKA No.K67819the first and the third authors were supported by Jedlik project “ReCoMend”2008-2011。
文摘In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.
文摘It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes? To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.
基金Research supported by NSF(No.11671231,11201262 and 10921101)Shandong Province(No.BS2013SF020 and ZR2014AP005)Young Scholars Program of Shandong University and the 111 Project(No.B12023).
文摘In this paper,we study the recursive stochastic optimal control problems.The control domain does not need to be convex,and the generator of the backward stochastic differential equation can contain z.We obtain the variational equations for backward stochastic differential equations,and then obtain the maximum principle which solves completely Peng’s open problem.
基金The first author was partially supported by Algerian CNEPRU Project Grant B01420130137,2014-2016.
文摘We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.
基金the National Nuclear Security Administration of the U.S.Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396the DOE Office of Science Advanced Scientific Computing Research(ASCR)Program in Applied Mathematics Research.The first author has been supported in part by the Czech Ministry of Education projects MSM 6840770022 and LC06052(Necas Center for Mathematical Modeling).
文摘The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems.The preservation of the qualitative characteristics,such as the maximum principle,in discrete model is one of the key requirements.It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular meshes in 2D.In this paper we consider how to enforce discrete maximum principle for linear finite element solutions for the linear second-order self-adjoint elliptic equation.First approach is based on repair technique,which is a posteriori correction of the discrete solution.Second method is based on constrained optimization.Numerical tests that include anisotropic cases demonstrate how our method works for problems for which the standard finite element methods produce numerical solutions that violate the discrete maximum principle.