In this paper we study one-dimensional generalized reflected backward stochastic differential equation with two barriers and stochastic quadratic growth. We prove the existence of a maximal solution when there exists a semimartingale between the barriers L and U , the generator f is continuous with general growth with respect to the variable y and stochastic quadratic growth with respect to the...

We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where both players control a continuous martingale. A similar representation as a control problem over discontinuous martingales was known for games with incomplete i...

Prefabricated housing and cast-in-site are two alternatives for selection by developers customers. The government, as the policy maker, creates incentive policies to encourage customers choose prefabricated housing. This paper aims analyze subsidy mechanism theoretically confirm subsidies’ scopes, amounts end times through an evolutionary game model simulation. In model, government subsidies af...

A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived from a given system by using the stochastic averaging method for quasi-Hamiltonian systems with u...

The risk of supply disruptions due to suppliers’ financial problems plays a prominent role in manufacturers’ risk portfolios. Even large suppliers (e.g. Delphi) could file for bankruptcy, and manufacturer’s actions, such as financial subsidies to the suppliers, affect profoundly suppliers’ financial health. Using a dynamic, stochastic, periodic-review model of the manufacturer’s joint capacity ...

Max-plus stochastic processes are counterparts of Markov diffusion processes governed by Ito sense stochastic differential equations. In this framework, expectations are linear operations with respect to max-plus arithmetic. Max-plus stochastic control problems are considered, in which a minimizing control enters the state dynamics and running cost. The minimum max-plus expected cost is equal t...

This paper studies two non-zero-sum stochastic differential games of control and stopping. One game has interaction in the players’ stopping rules, whereas the other does not. Solutions to backward stochastic differential equations (BSDEs) will be shown to provide the value processes of the first game. A multi-dimensional BSDE with reflecting barrier is studied in two cases for its solution: ex...

The Markov chain approximation method is a widely used, relatively easy to use, and efficient family of methods for the bulk of stochastic control problems in continuous time, for reßected-jump-diffusion type models. It has been shown to converge under broad conditions, and there are good algorithms for solving the numerical problems, if the dimension is not too high. We consider a class of sto...