| 1. |
- Agram, Nacira, 1987-, et al.
(författare)
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Stochastic control of memory mean-field processes
- 2019
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Ingår i: Applied mathematics and optimization. - : Springer. - 0095-4616 .- 1432-0606. ; 79:1, s. 181-204
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Tidskriftsartikel (refereegranskat)abstract
- By a memory mean-field process we mean the solution X(⋅)" role="presentation">X(⋅) of a stochastic mean-field equation involving not just the current state X(t) and its law L(X(t))" role="presentation">L(X(t)) at time t, but also the state values X(s) and its law L(X(s))" role="presentation">L(X(s)) at some previous times s<t." role="presentation">sM of measures on R" role="presentation">R with the norm ||⋅||M" role="presentation">||⋅||M introduced by Agram and Øksendal (Model uncertainty stochastic mean-field control. arXiv:1611.01385v5, [2]), and prove the existence and uniqueness of solutions of memory mean-field stochastic functional differential equations. We prove two stochastic maximum principles, one sufficient (a verification theorem) and one necessary, both under partial information. The corresponding equations for the adjoint variables are a pair of (time-advanced backward stochastic differential equations (absdes), one of them with values in the space of bounded linear functionals on path segment spaces. As an application of our methods, we solve a memory mean–variance problem as well as a linear–quadratic problem of a memory process.
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| 2. |
- Aiyappan, S., et al.
(författare)
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Homogenization of a Locally Periodic Oscillating Boundary
- 2022
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Ingår i: Applied Mathematics and Optimization. - : Springer Science and Business Media LLC. - 1432-0606 .- 0095-4616. ; 86:2
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The Neumann condition is prescribed on the oscillating part of the boundary, and the Dirichlet condition on a separate part. It is shown that the homogenization result holds in the sense of weak L2 convergence of the solutions and their flows, under natural hypothesis on the regularity of the domain. The strong L2 convergence of average preserving extensions of the solutions and their flows is also considered.
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| 3. |
- Andersson, Daniel, et al.
(författare)
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A maximum principle for SDEs of mean-field type
- 2011
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Ingår i: Applied mathematics and optimization. - : Springer Science and Business Media LLC. - 0095-4616 .- 1432-0606. ; 63:3, s. 341-356
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Tidskriftsartikel (refereegranskat)abstract
- We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
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| 4. |
- Andersson, Lars-Erik
(författare)
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Existence results for quasistatic contact problems with Coulomb friction
- 2000
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Ingår i: Applied mathematics and optimization. - : Springer Science and Business Media LLC. - 0095-4616 .- 1432-0606. ; 42:2, s. 169-202
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Tidskriftsartikel (refereegranskat)abstract
- We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved by the aid of an established shifting technique used to obtain increased regularity at the contact surface. The analysis is carried out by the aid of auxiliary problems involving regularized friction terms and a so-called normal compliance penalization technique.
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| 5. |
- Aronsson, Gunnar, et al.
(författare)
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L-infinity Variational Problems with Running Costs and Constraints
- 2012
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Ingår i: Applied mathematics and optimization. - : Springer Verlag (Germany). - 0095-4616 .- 1432-0606. ; 65:1, s. 53-90
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Tidskriftsartikel (refereegranskat)abstract
- Various approaches are used to derive the Aronsson-Euler equations for L-infinity calculus of variations problems with constraints. The problems considered involve holonomic, nonholonomic, isoperimetric, and isosupremic constraints on the minimizer. In addition, we derive the Aronsson-Euler equation for the basic L-infinity problem with a running cost and then consider properties of an absolute minimizer. Many open problems are introduced for further study.
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| 6. |
- Bahlali, Khaled, et al.
(författare)
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On the stochastic maximum principle in optimal control of degenerate diffusions with lipschitz coefficients
- 2007
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Ingår i: Applied mathematics and optimization. - : Springer Science and Business Media LLC. - 0095-4616 .- 1432-0606. ; 56:3, s. 364-378
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Tidskriftsartikel (refereegranskat)abstract
- We establish a stochastic maximum principle in optimal control of a general class of degenerate diffusion processes with global Lipschitz coefficients, generalizing the existing results on stochastic control of diffusion processes. We use distributional derivatives of the coefficients and the Bouleau Hirsh flow property, in order to define the adjoint process on an extension of the initial probability space.
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| 7. |
- Barth, A., et al.
(författare)
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Milstein approximation for advection-diffusion equations driven by multiplicative noncontinuous martingale noises
- 2012
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Ingår i: Applied Mathematics and Optimization. - : Springer Science and Business Media LLC. - 1432-0606 .- 0095-4616. ; 66:3, s. 387-413
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, càdlàg, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L2 and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler-Maruyama approximation. Finally, simulations complete the paper.© Springer Science+Business Media, LLC 2012.
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| 8. |
- Buckdahn, Rainer, et al.
(författare)
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A General Stochastic Maximum Principle for SDEs of Mean-field Type
- 2011
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Ingår i: Applied mathematics and optimization. - : Springer Science and Business Media LLC. - 0095-4616 .- 1432-0606. ; 64:2, s. 197-216
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Tidskriftsartikel (refereegranskat)abstract
- We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng's-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966-979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order adjoint equation remains the same as in Peng's stochastic maximum principle.
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| 9. |
- Christensen, Sören, 1982, et al.
(författare)
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Resolvent-Techniques for Multiple Exercise Problems
- 2015
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Ingår i: Applied Mathematics and Optimization. - : Springer Science and Business Media LLC. - 1432-0606 .- 0095-4616. ; 71:1, s. 95-123
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Tidskriftsartikel (refereegranskat)abstract
- © 2014, Springer Science+Business Media New York. We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristics of the problems can be identified more explicitly. We illustrate the main results with explicit examples.
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| 10. |
- De Angelis, Tiziano, et al.
(författare)
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Dynamic Programming Principle for Classical and Singular Stochastic Control with Discretionary Stopping
- 2023
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Ingår i: Applied mathematics and optimization. - : Springer Nature. - 0095-4616 .- 1432-0606. ; 88:1
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Tidskriftsartikel (refereegranskat)abstract
- We prove the dynamic programming principle (DPP) in a class of problems where an agent controls a d-dimensional diffusive dynamics via both classical and singular controls and, moreover, is able to terminate the optimisation at a time of her choosing, prior to a given maturity. The time-horizon of the problem is random and it is the smallest between a fixed terminal time and the first exit time of the state dynamics from a Borel set. We consider both the cases in which the total available fuel for the singular control is either bounded or unbounded. We build upon existing proofs of DPP and extend results available in the traditional literature on singular control (Haussmann and Suo in SIAM J Control Optim 33(3):916-936, 1995; SIAM J Control Optim 33(3):937-959, 1995) by relaxing some key assumptions and including the discretionary stopping feature. We also connect with more general versions of the DPP (e.g., Bouchard and Touzi in SIAM J Control Optim 49(3):948-962, 2011) by showing in detail how our class of problems meets the abstract requirements therein.
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