An optimality-equation for discrete stochastic decision problems with general sets of admissible strategies
P. Heinz-Müller (1985)
Banach Center Publications
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P. Heinz-Müller (1985)
Banach Center Publications
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Benchaabane, Abbes, Benchettah, Azzedine (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20. In this work we will study a problem of optimal investment in financial markets with stochastic volatility with small parameter. We used the averaging method of Bogoliubov for limited development for the optimal strategies when the small parameter of the model tends to zero and the limit for the optimal strategy and demonstrated the convergence of these optimal strategies.
Liangquan Zhang, Yufeng Shi (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short)....
Liangquan Zhang, Yufeng Shi (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short)....
Yufeng Shi, Qingfeng Zhu (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied...
Gianluca Gorni (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si studia il problema della sintesi per un problema di controllo stocastico con equazione di stato lineare e funzione costo convessa.
Ningombam Sanjib Meitei, Snigdha Banerjee (2013)
RAIRO - Operations Research - Recherche Opérationnelle
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Analysis of empirical sales data lead us to consider newsboy model for four practical market conditions arising from the presence/absence of stochastic lead time and exogenous linear temporal decline in selling price when distribution of the stochastic demand depends upon initial selling price. Viability of the solutions is discussed for three strategies of obtaining optimal initial selling price and/or ordering quantity. Numerical studies are conducted to assess the effects of lead...
Jianhui Huang, Na Li (2006)
Applicationes Mathematicae
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Herein, we develop a backward stochastic differential equation (BSDE) valuation of securities with default risk. Consequently, the optimal recovery problem with quasi-linear utility functions is discussed with the help of the stochastic maximum principle. Finally, two important examples: the exponential and power utility cases are studied and their business implications are considered.
Zhiyong Yu (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with...