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The maximality prin...
The maximality principle in singular control with absorption and its applications to the dividend problem
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- De Angelis, Tiziano (author)
- Univ Torino, Sch Management & Econ, Dept Econ Social Studies Appl Math & Stat, I-10134 Turin, Italy.;Coll Carlo Alberto, I-10122 Turin, Italy.,Department of Economics, Social Studies, Applied Mathematics, and Statistics, School of Management and Economics, University of Torino, Torino, Italy; Collegio Carlo Alberto, Torino, Italy
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- Ekström, Erik, 1977- (author)
- Uppsala universitet,Sannolikhetsteori och kombinatorik,Department of Mathematics, Uppsala University, Uppsala, Sweden
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- Olofsson, Marcus (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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Univ Torino, Sch Management & Econ, Dept Econ Social Studies Appl Math & Stat, I-10134 Turin, Italy;Coll Carlo Alberto, I-10122 Turin, Italy. Department of Economics, Social Studies, Applied Mathematics, and Statistics, School of Management and Economics, University of Torino, Torino, Italy; Collegio Carlo Alberto, Torino, Italy (creator_code:org_t)
- Society for Industrial and Applied Mathematics, 2024
- 2024
- English.
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In: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics. - 0363-0129 .- 1095-7138. ; 62:1, s. 91-117
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Abstract
Subject headings
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- Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with twodimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain nonlinear ODE. Contrarily to the classical one-dimensional formulation of the dividend problem, our framework produces a nontrivial solution when the firm's (predividend) equity capital evolves as a geometric Brownian motion. Such a solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- singular control with absorption
- maximality principle
- dividend problem
- optimal stopping
- free boundary problems
Publication and Content Type
- ref (subject category)
- art (subject category)
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