摘要本文研究了均值-方差优化准则下，保险人的最优投资和最优再保险问题.我们用一个复合泊松过程模型来拟合保险人的风险过程，保险人可以投资无风险资产和价格服从跳跃-扩散过程的风险资产.此外保险人还可以购买新的业务（如再保险）.本文的限制条件为投资和再保险策略均非负，即不允许卖空风险资产，且再保险的比例系数非负.除此之外，本文还引入了新巴塞尔协议对风险资产进行监管，使用随机二次线性（linear-quadratic，LQ）控制理论推导出最优值和最优策略.对应的哈密顿-雅克比-贝尔曼（Hamilton-Jacobi-Bellman，HJB）方程不再有古典解.在粘性解的框架下，我们给出了新的验证定理，并得到有效策略（最优投资策略和最优再保险策略）的显式解和有效前沿.
| | 服务 | |  | 加入引用管理器 | | E-mail Alert | | RSS | | 收稿日期: 2019-01-03 | | 基金资助:国家自然科学基金资助项目（11571189，11871219，11871220，11901201）；111引智计划（B14019）
| | 作者简介: 毕俊娜,E-mail:jnbi@sfs.ecnu.edu.cn;李旻瀚,E-mail:554136397@qq.com |
[1] Bai L., Zhang H., Dynamic mean-variance problem with constrained risk control for the insurers, Mathematical Methods of Operations Research, 2008, 68:181-205.
[2] Bäuerle N., Benchmark and mean-variance problems for insurers, Mathematical Methods of Operations Research, 2005, 62:159-165.
[3] Bi J., Cai J., Optimal investment-reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets, Insurance:Mathematics and Economics, 2019, 85:1-14.
[4] Bi J., Guo J., Optimal mean-variance problem with constrained controls in a jump-diffusion financial market for an insurer, Journal of Optimization Theory and Applications, 2013, 157(1):252-275.
[5] Browne S., Optimal investment policies for a firm with a random risk process:Exponential utility and minimizing the probability of ruin, Mathematics of Operations Research, 1995, 20:937-958.
[6] Delong L., Gerrard R., Mean-variance portfolio selection for a non-life insurance company, Mathematical Methods of Operations Research, 2007, 66:339-367.
[7] Fleming W. H., Soner H. M., Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, Berlin, 1993.
[8] Gaier J., Grandits P., Schachermayer W., Asymptotic ruin probabilities and optimal investment, Annals of Applied Probability, 2003, 13:1054-1076.
[9] Hipp C., Plum M., Optimal investment for insurers, Insurance:Mathematics and Economics, 2000, 27:215-228.
[10] Li X., Zhou X. Y., Lim A. E. B., Dynamic mean-variance portfolio selection with no-shorting constraints, SIAM Journal on Control and Optimization, 2002, 40:1540-1555.
[11] Lim A. E. B., Zhou X. Y., Mean-variance portfolio selection with random parameters in a complete market, Mathematics of Operations Research, 2002, 27:101-120.
[12] Levy H., Value-at-risk capital requirement regulation, risk taking and asset allocation:a mean-variance analysis, The European Journal of Finance, 2015, 21:21-241.
[13] Markowitz H., Portfolio selection, Journal of Finance, 1952, 7:77-91.
[14] Merton R. C., An analytical derivation of the efficient portfolio frontier, Journal of Financial and Quantitative Analysis, 1972, 7:1851-1872.
[15] Merton R. C., Theory of rational option pricing, Bell Journal of Economics and Management Science, 1973, 4:141-183.
[16] Schmidli H., On minimizing the ruin probability by investment and reinsurance, Annals of Applied Probability, 2002, 12:890-907.
[17] Schmidt T., Stute W., Shot-noise processes and the minimal martingale measure, Statistics and Probability Letters, 2007, 77:1332-1338.
[18] Wang Z., Xia J., Zhang L., Optimal investment for insurer with jump-diffusion risk process, Insurance:Mathematics and Economics, 2007, 40:322-334.
[19] Yong J. M., Zhou X. Y., Stochastic Controls:Hamilton Systems and HJB Equations, Springer-Verlag, New York, 1999.
[20] Zhou C., A jump-diffusion approach to modeling credit risk and valuing defaultable securities (March 1997), Finance and Economics Discussion Series, 1997-15, Board of Governors of the Federal Reserve System (U.S.), Available at SSRN:https://ssrn.com/abstract=39800 or http://dx.doi.org/10.2139/ssrn.39800
[21] Zhou X. Y., Li D., Continuous-time mean-variance portfolio selection:a stochastic LQ framework, Applied Mathematics and Optimization, 2000, 42:19-33.
[22] Zhou X. Y., Yong J., Li X., Stochastic verification theorems within the framework of viscosity solutions, SIAM Journal on Control and Optimization, 1997, 35:243-253.
|
PDF全文下载地址:
http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23551
非时齐马氏过程的Liggett-Stroock不等式宋娟1,张铭21.湖北经济学院信息管理与统计学院湖北金融发展与金融安全研究中心武汉430205;2.中国政法大学科学技术教学部北京102249Liggett-StroockInequalitiesforTimeInhomogeneousMarkov ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27超高维II型区间删失数据的非参数变量筛选法张婧1,靳韶佳2,陈丹丹21.中南财经政法大学统计与数学学院,武汉430073;2.武汉大学数学与统计学院,武汉430072NonparametricFeatureScreeningforUltrahigh-dimensionalCaseIIInterval ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27分组数据分位数回归模型的变量选择和估计刘栋1,杨冬梅2,何勇3,张新生41.上海财经大学统计与管理学院,上海200433;2.山东财经大学统计学院,济南250014;3.山东大学中泰证券金融研究院,济南250100;4.复旦大学管理学院,上海200433VariableSelectionandEst ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27部分信息下的投资决策的q理论黄文礼,杨可桢浙江财经大学中国金融研究院,杭州310018TheqTheoryofInvestmentDecisionUnderPartialInformationHUANGWenli,YANGKezhenChinaAcademyofFinancialResearch,Z ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27针对面板数据的半参数变系数可加模型的估计和推断崔晓静上海财经大学统计与管理学院,上海200433EstimationandInferenceofaSemiparametricVarying-coefficientAdditiveModelforPanelDataCUIXiaojingSchoolof ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27基于最小最大鞅测度对保险公司最优投资再保险问题的研究周子键,陈旭湖南师范大学数学与统计学院,长沙410081MiniMaxMartingaleMethodforOptimalInvestment-reinsuranceProbleminaGeneralInsuranceCompanyRiskMode ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27跨期的预防性努力投资决策研究-基于约束的Ross更加风险厌恶的刻画田有功1,柳江21.兰州财经大学信息工程学院,甘肃省电子商务技术与应用重点实验室,兰州730020;2.兰州财经大学经济学院,兰州730020IntertemporalInvestmentDecisionsonPrecautionar ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27偏正态数据下混合非线性位置回归模型的统计诊断曹幸运,聂兴锋,吴刘仓昆明理工大学理学院,昆明650093StatisticalDiagnosisofMixtureNonlinearLocationRegressionModelwithSkew-NormalDataCAOXingyun,NIEXingf ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27具有舍入误差微观结构噪音高频数据的杠杆效应分析蔺富明1,2,周勇31.上海财经大学统计与管理学院,上海,200433;2.四川轻化工大学数学与统计学院,自贡,643000;3.统计与数据科学前沿理论及应用教育部重点实验室华东师范大学统计交叉科学研究院,上海,200062AnalysisofLever ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27随机环境中两性分枝过程的矩收敛准则李应求,肖胜,彭朝晖长沙理工大学数学与统计学院,长沙410004MomentConvergenceCriteriaforBisexualBranchingProcessesinRandomEnvironmentsLIYingqiu,XIAOSheng,PENGZha ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27
|
