Electronic medical records and machine learning
Electronic medical record(EMR) has been widely used in China, which contains a lot of useful information. Data mining of EMRs can save medical resources, help to carry out preventive medicine, and finally improve the curative effect. There are many mathematical problems in the process of analyzing electronic medical records, such as incomplete data, unbalanced distribution, complex and highly nonlinear mathematical models, and so on. This lecture will introduce some of these problems and several current machine learning methods to solve them.
Refracted Lévy risk model with Parisian stochastic delays
An optimal dividend problem with transaction costs for an insurance company whose risk process evolves as a refracted Lévy process is atudied, in which the ruin time is determined by Parisian exponential delays and limited by a lower ultimate bankrupt barrier. In such a model, the existence of the transaction costs implies that this problem naturally turns to the impulse control problem associated with a control strategy. An important type of the control strategy is the impulse policy which means reducing the reserves to a certain level whenever they are above another level. Based on this, the value function which is used to measure the expected discounted utility of the impulse policy is explicitly expressed in terms of the Parisian refracted scale functions. More importantly, we can obtain both the necessary conditions and sufficient conditions such that the above described impulse policy is optimal for the impulse control problem, which involves the method to numerically find the optimal values of the levels. Finally, applications and numerical examples are presented, in which new analytical formulas for the Parisian refracted scale functions are derived in the cases of the Brownian risk process and the Cramér-Lundberg process with exponential claims. Then the main result is that there exists a unique impulse policy which is optimal for the impulse control problem. The numerical examples are also provided to illustrate some valuable conclusions for the refracted Lévy risk model.