Cramér--Lundberg模型下带随机系数的约束单调均值-方差投资-再保险问题

Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model

Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber-Shiu functions) in a Cramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as time dependant control functions, which leads to a setting from the theory of optimal stochastic control and ultimately to the problem's Hamilton-Jacobi-Bellman equation. We show existence and uniqueness of the solution found by this method and provide numerical examples involving light and heavy tailed claims and also give a remark on the asymptotics.

随机系数 Cramér-Lundberg 模型下的约束均值-方差投资-再保险

Constrained mean-variance investment-reinsurance under the Cramér-Lundberg model with random coefficients

研究随机系数 Cramér-Lundberg 模型中凸锥约束下的均值-方差投资-再保险问题，利用带跳 BSDE 技术证明 SREs 解唯一，并显式得到线性反馈有效策略与半直线有效前沿。

Optimizing expected utility of dividend payments for a Cramér-Lundberg risk proces

We consider the problem of maximizing the discounted utility of dividend payments of an insurance company whose reserves are modeled as a classical Cramér-Lundberg risk process. We investigate this optimization problem under the constraint that dividend rate is bounded. We prove that the value function fulfills the Hamilton-Jacobi-Bellman equation and we identify the optimal dividend strategy.

分红累积与资本注入在Cramér-Lundberg模型下：强解与最优策略

Dividend ratcheting and capital injection under the Cramér-Lundberg model: Strong solution and optimal strategy

本文研究保险公司在经典Cramér-Lundberg模型下考虑分红率累积约束和资本注入的最优分红问题，通过构造偏积分变分不等式方程并证明强解存在性，提出无切换自由边界和显式反馈控制策略，为经济中的分红政策设计提供数学理论基础。

Optimal Constrained Investment in the Cramer-Lundberg model

We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation. There is a constraint that the insurance company can only invest in the risky asset at a limited leveraging level; more precisely, when purchasing, the ratio of the investment amount in the risky asset to the surplus level is no more than a; and when shortselling, the proportion of the proceeds from the short-selling to the surplus level is no more than b. The objective is to…

Optimal dividend payment under time of ruin contraint: Exponential case

We consider the classical optimal dividends problem under the Cramér-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the optimal value function can be obtained as the point-wise infimum of auxiliary value functions indexed by Lagrange multipliers. We also present a series of numerical examples.