The Optimal Dynamic Reinsurance Strategies in Multidimensional Portfolio

偿付能力约束下的最优再保险设计

Optimal reinsurance design under solvency constraints

本文利用鞅方法，在偿付能力约束（下界、VaR和CVaR）下，求解最大化盈余终值二次效用的最优再保险设计，发现其为比例保护与止损保护的组合，并与金融最优组合对比。

Equity Allocation and Portfolio Selection in Insurance

A discrete time probabilistic model, for optimal equity allocation and portfolio selection, is formulated so as to apply to (at least) reinsurance. In the context of a company with several portfolios (or subsidiaries), representing both liabilities and assets, it is proved that the model has solutions respecting constraints on ROE's, ruin probabilities and market shares currently in practical use. Solutions define global and optimal risk management strategies of the company. Mathematical existence results and tools, such as the inversion of the linear part of the Euler-Lagrange equations, deve…

Optimal Rebalancing Frequencies for Multidimensional Portfolios

We study optimal investment with multiple assets in the presence of small proportional transaction costs. Rather than computing an asymptotically optimal no-trade region, we optimize over suitable trading frequencies. We derive explicit formulas for these and the associated welfare losses due to small transaction costs in a general, multidimensional diffusion setting, and compare their performance to a number of alternatives using Monte Carlo simulations.

关于一类最优再保险问题

On a Class of Optimal Reinsurance Problems

本文研究了一类最优再保险问题，通过凸分析工具，将约束优化与惩罚优化等价，并提出用不同方法求解方差、CVaR和VaR作为风险度量的解决方案。

Constrained stochastic LQ control with regime switching and application to portfolio selection

This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients, and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and the Markov chain. Using Itô's lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ESREs). We prove the existence and uniqueness of the two ESREs using tools including multidimensional comparison theorem, truncation function technique, log transform…

多维不定随机 Riccati 方程与具有非 Markov 机制切换的零和随机线性二次微分博弈

Multidimensional indefinite stochastic Riccati equations and zero-sum stochastic linear-quadratic differential games with non-Markovian regime switching

针对非 Markov 机制切换下的零和随机线性二次微分博弈，本文借助新型多维不定 SRE 与无界系数线性 BSDE 给出闭环最优策略，并证明该 SRE 解的存在唯一性。