报 告 人：王文元，男，厦门大学数学科学学院副教授、博士生导师

报告时间：2023年4月21日（周五）下午3点-4点

报告地点：#腾讯会议：877-662-173

报告摘要：In this talk, De Finetti's optimal dividend problem with capital injection under spectrally positive Markov additive models is studied. Based on dynamic programming principle, we first study an auxiliary singular control problem with a final payoff at an exponential random time. The double barrier strategy is shown to be optimal and the optimal barriers are characterized in analytical form using fluctuation identities of spectrally positive Lévy processes. We then transform the original problem under spectrally positive Markov additive models into an equivalent series of local optimization problems with the final payoff at the regime-switching time. The optimality of the regime-modulated double barrier strategy can be confirmed for the original problem using results from the auxiliary problem and the fixed point argument for recursive iterations.

报告人简介：王文元，男，博士，厦门大学数学科学学院副教授、博士生导师。主要研究方向有保险金融数学、概率论与随机过程、随机控制与优化。目前主要研究兴趣有马氏可加过程下的最优控制问题和基于机器学习的随机控制问题。近年来以第一或通讯作者身份在保险精算领域杂志Insurance Math. Econom./ Scand. Actuar. J./Eur. Actuar. J.，理论与应用概率领域杂志J. Theoret. Probab./Adv. in Appl. Probab./ J. Appl. Probab./Extremes，随机控制领域杂志J. Optim. Theory Appl.等上发表科研论文40余篇。主持国家自然科学基金项目3项。2017年入选福建省新世纪优秀人才支持计划。