奇异Hamilton-Jacobi-Bellman方程粘性解的存在唯一性

EXISTENCE AND UNIQUENESS OF THE VISCOSITY SOLUTION TO SOME SINGULAR HJB EQUATIONS

研究系数在边界点有奇性的一类Hamilton-Jacobi-Bellman(HJB)方程的粘性解的存在唯一性问题及解的渐近估计,这类问题包括波动系数振荡或爆破的情况.奇异HJB方程在随机最优控制和金融数学等许多领域都有重要的应用,包括金融数学中的随机利率模型.应用粘性上下解理论建立了一类奇异HJB方程的比较原理,给出了粘性解存在唯一性的条件.

This paper is considered with the existence and uniqueness of the viscosity solution to some Hamilton-Jacobi-Bellman （HJB） equations with singular coefficients near at the boundary with either vanishing, or oscillating, or blowing-up diffusion coefficients. The singular HJB equation has been applied to stochastic optimal control and financial mathematics, including stochastic rate CIR model. By means of viscosity super-solution and viscosity sub- solution theory, the comparison principle of viscosity solution to the singular HJB equation is obtained, and the conditions of the existence and uniqueness of the solution are given.