论文标题
在再保险中，线性化技术和一类混合奇异/连续控制问题的双重算法。第一部分：理论方面
Linearisation Techniques and the Dual Algorithm for a Class of Mixed Singular/Continuous Control Problems in Reinsurance. Part I: Theoretical Aspects
论文作者
论文摘要
本文着重于一类混合奇异/连续控制问题和随后的算法的线性化技术。动机来自（重新）保险问题，依赖于储备金的保费，并通过允许奇异的股息支付和资本注射来提出cram {é} r-lundberg索赔。使用变分技术并将轨迹嵌入适当的职业措施中，我们提供了这种问题的线性化，在这种问题中，再保险策略和奇异策略通过股息和资本注射给出了连续控制。线性化转化为双动力编程（DDP）算法。本文的重要部分致力于结构上的考虑，允许合理实施。我们还暗示了依赖于正方形和LMI（线性矩阵不等式）的矩和LMI的连接，以近似最佳候选物。
This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cram{é}r-Lundberg claims, by allowing singular dividend payments and capital injections. Using variational techniques and embedding the trajectories in an appropriate family of occupation measures, we provide the linearisation of such problems in which the continuous control is given by reinsurance policies and the singular one by dividends and capital injections. The linearisation translates into a dual dynamic programming (DDP) algorithm. An important part of the paper is dedicated to structural considerations allowing reasonable implementation. We also hint connections to methods relying on moment sum of squares and LMI (linear matrix inequality)-relaxations to approximate the optimal candidates.
