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Malliavin method for optimal investment in financial markets with memory

Qiguang An, Guoqing Zhao, Gaofeng Zong (2016)

Open Mathematics

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 market....

Marginal problem, statistical estimation, and Möbius formula

Martin Janžura (2007)

Kybernetika

A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood...

Markov decision processes with time-varying discount factors and random horizon

Rocio Ilhuicatzi-Roldán, Hugo Cruz-Suárez, Selene Chávez-Rodríguez (2017)

Kybernetika

This paper is related to Markov Decision Processes. The optimal control problem is to minimize the expected total discounted cost, with a non-constant discount factor. The discount factor is time-varying and it could depend on the state and the action. Furthermore, it is considered that the horizon of the optimization problem is given by a discrete random variable, that is, a random horizon is assumed. Under general conditions on Markov control model, using the dynamic programming approach, an optimality...

Maximum principle for forward-backward doubly stochastic control systems and applications

Liangquan Zhang, Yufeng Shi (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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). And as an example...

Maximum principle for forward-backward doubly stochastic control systems and applications*

Liangquan Zhang, Yufeng Shi (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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). And as an...

Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations

Jianhui Huang, Jingtao Shi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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 quadratic...

Mean stability of a stochastic difference equation

Viorica Mariela Ungureanu, Sui Sun Cheng (2008)

Annales Polonici Mathematici

A simple personal saving model with interest rate based on random fluctuation of national growth rate is considered. We establish connections between the mean stochastic stability of our model and the deterministic stability of related partial difference equations. Then the asymptotic behavior of our stochastic model is studied. Although the model is simple, the techniques for obtaining its properties are not, and we make use of the theory of abstract Banach algebras and weighted spaces. It is hoped...

Memoryless solution to the optimal control problem for linear systems with delayed input

Francesco Carravetta, Pasquale Palumbo, Pierdomenico Pepe (2013)

Kybernetika

This note investigates the optimal control problem for a time-invariant linear systems with an arbitrary constant time-delay in in the input channel. A state feedback is provided for the infinite horizon case with a quadratic cost function. The solution is memoryless, except at an initial time interval of measure equal to the time-delay. If the initial input is set equal to zero, then the optimal feedback control law is memoryless from the beginning. Stability results are established for the closed...

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