基于相关性的保险人的投资与再保险的理论和方法研究

本项目将在保险盈余过程与风险资产价格过程存在相关性的条件下，系统探讨保险人的最优投资和最优再保险问题。项目将在阐述保险投资、再保险研究的进展及存在的主要问题的基础上，探讨有保险盈余过程影响的保险人的最优投资与再保险研究的理论和方法。项目将重点考虑：1）保险人投资的多种风险资产价格过程服从几何Brownian运动且与保险盈余过程相关时，保险人的最优投资与再保险问题及相应的因素分析；2）在投资的风险资产具有随机波动率且与保险盈余过程相关时，保险人的最优投资与再保险问题；3）在保险盈余过程与风险资产价格过程相关情况下，探讨二基金定理是否成立或成立的条件，进而研究有保险盈余过程影响的、投资于多种风险资产的保险人的最优投资与再保险问题；4）随机利率环境下，考虑保险盈余过程影响的保险人的最优投资与再保险问题；5）兼顾保险人与再保险人利益，考虑保险盈余过程影响的保险人的最优投资与再保险问题。

This project will study the problem of insurer’s optimal investment and optimal reinsurance, when the price process of risky assets and insurance surplus process are dependent. We shall expound the research progress and the primal problem of insurance investment and reinsurance, discuss the theory and methods of insurance investment and reinsurance. We shall discuss: 1) insurer’s optimal investment decision, optimal reinsurance and factor analysis with multiple risky assets under geometry Brownian motion in the case of influence of insurance surplus process. 2) insurer’s optimal investment and optimal reinsurance, when risky assets have stochastic volatility and are dependent on insurance surplus process. 3) whether the two fund theorem holds or not, or conditions of establishment of the two fund theorem, when the price process of risky assets and insurance surplus process are dependent, then study insurer’s optimal investment and reinsurance with multiple risky assets. 4) insurer’s optimal investment and optimal reinsurance with influence of insurance surplus return process under stochastic interest rate; 5) balance the interests of the insurer and reinsurer, insurer’s optimal investment and optimal reinsurance with influence of insurance surplus process.