Controlled Switching Diffusions Under Ambiguity: The Average Criterion

International Game Theory Review ◽

10.1142/s0219198921500171 ◽

2021 ◽

pp. 2150017

Author(s):

Beatris A. Escobedo-Trujillo ◽

Carmen G. Higuera-Chan ◽

José Daniel López-Barrientos

Keyword(s):

Diffusion Process ◽

Control Problem ◽

Unknown Parameter ◽

Controlled Switching ◽

Switching Diffusions ◽

Central Controller ◽

Average Criterion ◽

Drift Coefficient

This paper concerns controlled switching diffusions. In particular, we consider that the drift coefficient of the diffusion process depends on an unknown (and possibly nonobservable) parameter. For giving solution to our control problem, we formulate it as a game against nature, where the ambiguity is represented by nature that chooses values of the unknown parameter through actions so playing the role as an opposite player of the controller. Our objective is to give conditions to characterize the ergodic optimality and guarantee the existence of optiaml policies for the central controller. Finally, we provide two examples to illustrate our results.

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Variational Iteration Method for a Nonlinear Reaction-Diffusion Process

International Journal of Chemical Reactor Engineering ◽

10.2202/1542-6580.1630 ◽

2008 ◽

Vol 6 (1) ◽

Cited By ~ 3

Author(s):

Shu-Qiang Wang ◽

Ji-Huan He

Keyword(s):

Exact Solution ◽

Diffusion Process ◽

Iteration Method ◽

Unknown Parameter ◽

Reaction Diffusion ◽

Variational Iteration Method ◽

Rigorous Derivation ◽

Variational Iteration ◽

Nonlinear Reaction ◽

The Given

An extremely simple and elementary, but rigorous derivation of temperature distribution of a reaction-diffusion process is given using the variational iteration method. In this method, a trial function (an initial solution) is chosen with some unknown parameter, which is identified after a few iterations according to the given boundary conditions. Comparison with the exact solution shows that the method is very effective and convenient.

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An Optimal Portfolio Problem of DC Pension with Input-Delay and Jump-Diffusion Process

Mathematical Problems in Engineering ◽

10.1155/2020/4343629 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Weixiang Xu ◽

Jinggui Gao

Keyword(s):

Diffusion Process ◽

Control Problem ◽

Jump Diffusion ◽

Investment Strategy ◽

Optimal Portfolio ◽

Input Delay ◽

Programming Approach ◽

Time Interval ◽

Stochastic Dynamic ◽

Jump Diffusion Process

In this paper, an optimal portfolio control problem of DC pension is studied where the time interval between the implementation of investment behavior and its effectiveness (hereafter input-delay) is particularly focused. There are two assets available for investment: a risk-free cash bond and a risky stock with a jump-diffusion process. And the wealth process of the pension fund is modeled as a stochastic delay differential equation. To secure a comfortable retirement life for pension members and also avoid excessive risk, the fund managers in this paper aim to minimize the expected value of quadratic deviations between the actual terminal fund scale and a preset terminal target. By applying the stochastic dynamic programming approach and the match method, the optimal portfolio control problem is solved and the closed-form solution is obtained. In addition, an algorithm is developed to calculate the numerical solution of the optimal strategy. Finally, we have performed a sensitivity analysis to explore how the managers’ preset terminal target, the length of input-delay, and the jump intensity of risky assets affect the optimal investment strategy.

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