在不允许卖空条件下的最优比例再保险投资

假设保险公司的盈余过程服从一个带扰动项的布朗运动,保险公司可以投资一个无风险资产和n个风险资产,还可以购买比例再保险,并且风险市场是不允许卖空的.本文在均值一方差优化准则下研究保险公司的最优投资一再保策略选择问题,利用LQ随机控制方法求解模型,得到了保险公司的最优组合投资策略的解析和保险公司投资的有效投资边界的解析表达...     

马尔可夫市场中的一般多期均值-方差资产负债管理问题的时间一致策略

文章在多期均值-方差框架下研究一个带马尔可夫机制转换及跨期目标控制的一般资产负债管理问题.随机的风险资产收益率和外生负债增长率均依赖于有限多个服从离散时间马尔可夫链的金融市场状态.在投资过程中投资者不仅要考虑终端盈余的均值-方差效用,还需要同时关注中间目标效用的控制.以最大化每时刻盈余的均值-方差效用的加权总和为目标,文章构建了一般的多期均值-方差资产负债管理模型.在博弈论框架下,利用逆向归纳法,文章导出了问题的时间一致策略、均衡值函数及时间一致策略下每时刻盈余的期望和方差的解析表达式,并讨论了几种退化情形下的均衡结果.最后,文章通过数值例子揭示了机制转换、负债对均衡有效前沿的影响以及跨期目标控制对资产负债管理的作用.     

机构投资者的最优持仓策略研究

讨论了机构投资者的最优持仓策略问题,假设证券价格服从几何布朗运动,以均值方差效用为目标函数,得到了最优持仓策略所满足的二阶微分方程,并由差分法得到其数值解.最后,由参数的敏感性分析知:最优持仓策略与瞬时冲击、市场波动率及风险厌恶系数等参数有关,并分析了参数变化对最优持仓策略的影响.     

道德风险影响下的保险最优投资研究

在考虑道德风险的情况下,以均值方差准则为目标研究保险人最优投资问题.假设保险盈余过程服从C-L模型,金融市场上存在一种无风险资产和一种风险资产可供投资,其中风险资产的价格过程服从几何布朗运动.在纯道德风险保险契约设计中,借鉴相关研究对努力水平和效用化努力成本的假设,量化道德风险对盈余过程的影响.在均值方差目标下,建立保险人最优投资问题的广义Hamilton-Jacobi-Bellman(HJB)方程,给出保险人时间一致的均衡投资策略和价值函数.结果显示累计索赔比例参数越大,公司对最优努力水平越敏感,采取措施降低道德风险有利于公司收益提升;努力成本参数越大,公司会降低努力水平减少支出,避免损失.     

均值-方差准则下具有负债的随机微分博弈

研究了均值-方差准则下,具有负债的随机微分博弈.研究目标是:在终值财富的均值等于k的限制下,在市场出现最坏的情况下找到最优的投资策略使终值财富的方差最小.即:基于均值-方差随机微分博弈的投资组合选择问题.使用线性-二次控制的理论解决了该问题,获得了最优的投资策略、最优市场策略和有效边界的显示解.并通过对所得结果进行进一步分析,在经济上给出了进一步的解释.通过本文的研究,可以指导金融公司在面临负债和金融市场情况恶劣时,选择恰当的投资策略使自身获得一定的财富而面临的风险最小.     

再保险-投资的M-V及M-VaR最优策略

考虑保险公司再保险-投资问题在均值-方差(M-V)模型和均值-在险价值(M-VaR)模型下的最优常数再调整策略.在保险公司盈余过程服从扩散过程的假设及多风险资产的Black-Scholes市场条件下,分别得到均值-方差模型和均值-在险价值模型下保险公司再保险-投资问题的最优常数再调整策略及共有效前沿,并就两种模型下的结...     

Heston随机波动率模型下的资产负债管理问题

应用随机最优控制方法研究Heston随机波动率模型下带有负债过程的动态投资组合问题,其中假设股票价格服从Heston随机波动率模型,负债过程由带漂移的布朗运动所驱动.金融市场由一种无风险资产和一种风险资产组成.应用随机动态规划原理和变量替换法得出了上述问题在幂效用和指数效用函数下最优投资策略的显示解,并给出数值算例分别分析了市场参数在幂效用和指数效用函数下对最优投资策略的影响.     

风险资产价格服从CEV模型的投资组合随机微分博弈

本文在风险资产价格服从CEV模型时,讨论两个投资者的时间一致均值-方差最优投资组合选择的随机微分博弈问题.运用动态规划原理,求得了最优投资策略及相应的值函数.     

不同模型下ES风险度量的计算

给出当金融资产遵从几何布朗运动时期望损失的计算。当金融资产价格的对数收益率服从均值方程为ARMA模型,方差方程为GARCH(s,n)模型,而均值修正后的收益率分别服从正态分布、t分布和GED分布时,给出了期望损失的计算。     

连续时间Markov决策过程的均值-方差优化问题

本文考虑连续时间Markov决策过程折扣模型的均值-方差优化问题.假设状态空间和行动空间均为Polish空间,转移率和报酬率函数均无界.本文的优化目标是在折扣最优平稳策略类里,选取相应方差最小的策略.本文致力于寻找Polish空间下Markov决策过程均值-方差最优策略存在的条件.利用首次进入分解方法,本文证明均值-方差优化问题可以转化为"等价"的期望折扣优化问题,进而得到关于均值-方差优化问题的"最优方程"和均值-方差最优策略的存在性以及它相应的特征.最后,本文给出若干例子说明折扣最优策略的不唯一性和均值-方差最优策略的存在性.     

Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market

This paper considers a non-self-financing mean-variance portfolio selection problem in which the stock price and the stochastic cash flow follow a Markov-modulated Lévy process and a Markov-modulated Brownian motion with drift, respectively. The stochastic cash flow can be explained as the stochastic income or liability of the investors during the investment process. The existence of optimal solutions is analyzed, and the optimal strategy and the efficient frontier are derived in closed-form by the Lagrange multiplier technique and the LQ (Linear Quadratic) technique.     

Robust mean variance portfolio selection model in the jump-diffusion financial market with an intractable claim

In this paper, a continuous-time robust mean variance model in the jump-diffusion financial market with an intractable claim is considered, in which the price processes of the assets not only are driven by the Brownian motion, but also have the Poisson jumps. By combining the martingale representation theorem and the quantile formulation method, an explicit closed-form solution of the robust mean-variance portfolio selection model is given under some suitable assumptions.     

Continuous-time mean–variance portfolio selection with liability and regime switching

A continuous-time mean–variance model for individual investors with stochastic liability in a Markovian regime switching financial market, is investigated as a generalization of the model of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean–variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466–1482]. We assume that the risky stock’s price is governed by a Markovian regime-switching geometric Brownian motion, and the liability follows a Markovian regime-switching Brownian motion with drift, respectively. The evolution of appreciation rates, volatility rates and the interest rates are modulated by the Markov chain, and the Markov switching diffusion is assumed to be independent of the underlying Brownian motion. The correlation between the risky asset and the liability is considered. The objective is to minimize the risk (measured by variance) of the terminal wealth subject to a given expected terminal wealth level. Using the Lagrange multiplier technique and the linear-quadratic control technique, we get the expressions of the optimal portfolio and the mean–variance efficient frontier in closed forms. Further, the results of our special case without liability is consistent with those results of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean–variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466–1482].     

Continuous-time portfolio selection with liability: Mean–variance model and stochastic LQ approach

In this paper we formulate a continuous-time mean–variance portfolio selection model with multiple risky assets and one liability in an incomplete market. The risky assets’ prices are governed by geometric Brownian motions while the liability evolves according to a Brownian motion with drift. The correlations between the risky assets and the liability are considered. The objective is to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. We derive explicitly the optimal dynamic strategy and the mean–variance efficient frontier in closed forms by using the general stochastic linear-quadratic (LQ) control technique. Several special cases are discussed and a numerical example is also given.     

Mean-variance portfolio selection for a non-life insurance company

We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market consisting of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise. We investigate two optimization problems. The first one is the classical mean-variance portfolio selection. In this case the efficient frontier is derived. The second optimization problem, except the mean-variance terminal objective, includes also a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target which is a random process. In order to find optimal strategies we apply techniques from the stochastic control theory.     

Mean-variance optimization problems for an accumulation phase in a defined benefit plan

In this paper we deal with contribution rate and asset allocation strategies in a pre-retirement accumulation phase. We consider a single cohort of workers and investigate a retirement plan of a defined benefit type in which an accumulated fund is converted into a life annuity. Due to the random evolution of a mortality intensity, the future price of an annuity, and as a result, the liability of the fund, is uncertain. A manager has control over a contribution rate and an investment strategy and is concerned with covering the random claim. We consider two mean-variance optimization problems, which are quadratic control problems with an additional constraint on the expected value of the terminal surplus of the fund. This functional objectives can be related to the well-established financial theory of claim hedging. The financial market consists of a risk-free asset with a constant force of interest and a risky asset whose price is driven by a Lévy noise, whereas the evolution of a mortality intensity is described by a stochastic differential equation driven by a Brownian motion. Techniques from the stochastic control theory are applied in order to find optimal strategies.     

Optimal time-consistent investment and reinsurance policies for mean-variance insurers

This paper investigates the optimal time-consistent policies of an investment-reinsurance problem and an investment-only problem under the mean-variance criterion for an insurer whose surplus process is approximated by a Brownian motion with drift. The financial market considered by the insurer consists of one risk-free asset and multiple risky assets whose price processes follow geometric Brownian motions. A general verification theorem is developed, and explicit closed-form expressions of the optimal polices and the optimal value functions are derived for the two problems. Economic implications and numerical sensitivity analysis are presented for our results. Our main findings are: (i) the optimal time-consistent policies of both problems are independent of their corresponding wealth processes; (ii) the two problems have the same optimal investment policies; (iii) the parameters of the risky assets (the insurance market) have no impact on the optimal reinsurance (investment) policy; (iv) the premium return rate of the insurer does not affect the optimal policies but affects the optimal value functions; (v) reinsurance can increase the mean-variance utility.     

考虑交易费用和债务的再保险和投资问题

该文考虑了保险公司的再保险和投资在多种风险资产中的策略问题. 假设保险公司本身有着一定的债务, 债务的多少服从线性扩散方程. 保险公司可以通过再保险和将再保险之后的剩余资产投资在m种风险资产和一种无风险资产中降低其风险. 资产中风险资产的价格波动服从几何布朗运动, 其债务多少的演化也是依据布朗运动而上下波动. 该文考虑了风险资产与债务之间的相互关系, 考虑了在进行风险投资时的交易费用, 并且利用HJB方程求得保险公司的最大最终资产的预期指数效用, 给出了相应的最优价值函数和最优策略的数值解.