Xiaoqing Pan, Xiaohu Li (2017)
Dependence Modeling
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This paper studies the increasing convex ordering of the optimal discounted capital allocations for stochastic arrangement increasing risks with stochastic arrangement decreasing occurrence times. The application to optimal allocation of policy limits is presented as an illustration as well.
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)....
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...
S. Trybuła, K. Szajowski (1987)
Applicationes Mathematicae
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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.
Liangquan Zhang, Yufeng Shi (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
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)....
Qiguang An, Guoqing Zhao, Gaofeng Zong (2016)
Open Mathematics
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We consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial...
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...
Stefan Ankirchner, Thomas Kruse (2015)
Banach Center Publications
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We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the...
Jianhui Huang, Jingtao Shi (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear...