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Ming-hui Wang

Publications and source records attributed to Ming-hui Wang.

5 recordsLinked to original sources
arXiv2024

Optimal Control Problems Governed by MFSDEs with multi-defaults

In this paper, we solve an optimal control problem governed by a system of mean-field stochastic differential equations with multiple defaults (MMFSDEs). We transform the global optimal control problem into several optimal control subproblems governed by a system of mean-field stochastic differential equations with single default (SMFSDEs) and derive both the sufficient and necessary maximum principles for these subproblems. We also give the existence and uniqueness of solutions to the MMFSDEs and the mean-field backward stochastic differential equations with multiple defaults (MMFBSDEs), respectively. Finally, as an example, our results are applied to obtain the explicit solution for an optimal control problem whose cost function is considered as a recursive utility process with multiple defaults.

math.OC↗
arXiv2021

A Linear-quadratic Mean-Field Stochastic Stackelberg Differential Game with Random Exit Time

In this paper, we investigate a new model of a linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which the leader is allowed to stop her strategy at a random time. Our overarching goal is to find the Stackelberg solution of the leader and followers for such a model. By employing the backward induction method, the state equation is divided into two-stage equations. Moreover, by using the maximum principle and the verification theorem, the Stackelberg solution is obtained for such a model.

math.OC↗
arXiv2020

A stochastic optimal control problem governed by SPDEs via a spatial-temporal interaction operator

In this paper, we first introduce a new spatial-temporal interaction operator to describe the space-time dependent phenomena. Then we consider the stochastic optimal control of a new system governed by a stochastic partial differential equation with the spatial-temporal interaction operator. To solve such a stochastic optimal control problem, we derive an adjoint backward stochastic partial differential equation with spatial-temporal dependence by defining a Hamiltonian functional, and give both the sufficient and necessary (Pontryagin-Bismut-Bensoussan type) maximum principles. Moreover, the existence and uniqueness of solutions are proved for the corresponding adjoint backward stochastic partial differential equations. Finally, our results are applied to study the population growth problems with the space-time dependent phenomena.

math.OC↗
arXiv2018

Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity

In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous model. Moreover, discrete and continuous sampled volatility swap pricing formulas are given by employing transform techniques and the relationship between two pricing formulas is discussed. Finally, some numerical simulations are reported to support the results presented in this paper.

q-fin.PR↗