Max-plus probabilistic approach to problems related to stochasitic control

Max-plus代数是分别用最大值和实数的加法代替传统的加法和乘法得到的。利用max-plus代数研究连续时间和连续状态控制问题，得到了随机和确定性控制下动态规划偏微分方程解的结构和值函数的刻画的新结果。这些结果基于max-plus方法。从最大加概率的角度出发，提出了数学金融学中的最优消费和最优投资问题，并对最优值进行了刻画。

Max-plus algebra is obtained by replacing the conventional addition and multiplication with maximum and the addition in reals, respectively. Using max-plus algebra in continuous-time and continuum-state control problems, we obtained new results on structures of solutions and characterizations of value functions for dynamic programming partial differential equations in stochastic and deterministic controls. These results are based on max-plus methodology. We also formulated optimal consumption and investment problems in mathematical finance by max-plus probabilistic point of view and characterized optimal values.