方差保费准则下的最优脉冲控制

本文研究保险公司在有再保险控制下的最优脉冲分红问题. 对保险公司的理赔损失, 假定有两家再保险公司参与分保, 且保险公司与两家再保险公司采取不同参数下的方差保费准则. 进一步, 假定保险公司有股东红利分配, 且每次分红有固定交易费和比例税收, 即脉冲分红. 在扩散逼近模型下, 本文应用随机动态规划方法研究破产前的最大期望折现分红, 给出值函数的解析表达式, 进而获得最优再保险策略和分红策略的具体形式.     

Implied Filtering Densities on the Hidden State of Stochastic Volatility

Abstract

We formulate and analyse an inverse problem using derivative prices to obtain an implied filtering density on volatility’s hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional expectations that are already observed in the market, and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as separability. This specification has a multiplicative component that behaves like a risk premium on volatility uncertainty in the market. When applied to SPX options data, the estimated model and implied densities produce variance-swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur due to the options’ expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options.     

Computation of the random arrival rule for bankruptcy problems

Bankruptcy problems are a fundamental class of fair division problems in microeconomics. Among the various solution concepts proposed for the problem, the random arrival rule is one of the most prominent. In this paper, we conduct a computational analysis of the rule. It is shown that the allocation returned by the rule is #P-complete to compute. The general complexity result is complemented by a pseudo-polynomial-time dynamic programming algorithm for the random arrival rule.     

A multiperiod model for estimating the cost of deposit insurance under the Basel III minimum capital requirement

Under the Basel III regime, a commercial bank is considered adequately capitalized if it maintains a ratio of capital to total risk-weighted assets or capital adequacy ratio (CAR) of at least 8%. We model a commercial bank that complies with Basel III's minimum capital requirement on an interval $[0,T]$ for $T>0$. The bank model is achieved via a specific rate of capital influx that fixes the bank's CAR at the minimum prescribed level of 8%. On the basis of this capital influx rate, we derive models for the bank's asset portfolio and capital dynamics required for maintaining the CAR at the minimum prescribed level. For the aforementioned bank, we further study a deposit insurance (DI) pricing problem with a coverage horizon equal to $T$ years. More specifically, we employ a multiperiod DI pricing model to approximate the cost of DI for the bank on the interval $[0,T]$, where the constant (minimum) CAR is maintained. We study the behaviours of the models leading to the constant (minimum) CAR, and the behaviour of the DI premium estimate by means of numerical simulations. In the simulation study pertaining to the DI premium estimate specifically, we determine the effects of changes in the bank's initial leverage level (deposit-to-asset ratio), the DI coverage horizon, and the volatility of the asset portfolio on the DI premium estimate.     

Estimating the distortion parameter of the proportional hazards premium for heavy-tailed losses under Lévy-stable regime

Estimating the distorted parameter in the case of non negative heavy-tailed losses has been treated in Brahimi et al. (2011). In this paper, we extend this work to the case of the real heavy-tailed losses. We derive an asymptotic distribution of the estimator. We construct a practically implemented confidence interval for the distortion parameter and illustrate the performance of the interval in a simulation study with application to real data.     

The expected discounted penalty function under a risk model with stochastic income

Quantities of interest in ruin theory are investigated under the general framework of the expected discounted penalty function, assuming a risk model where both premiums and claims follow compound Poisson processes. Both a defective renewal equation and an integral equation satisfied by the expected discounted penalty function are established. Some implications that these equations have on particular quantities such as the discounted deficit and the probability of ultimate ruin are illustrated. Finally, the case when premiums have Erlang(n,β) distribution and the distribution of the claims is arbitrary is investigated in more depth. Throughout the paper specific examples where claims and premiums have particular distributions are provided.     

The uncertainties about the relationships risk–return–volatility in the Spanish stock market

The relationships between the market risk premium, its conditional variance and the risk-free rate in the Spanish stock market are studied in this paper. Using daily data, the above mentioned relations are analyzed by quasi maximum likelihood for an EGARCH-M(1,1) model with normal innovations and by nonparametric maximum likelihood for a semiparametric EGARCH-M(1,1) model with arbitrarily distributed innovations. It is worth mentioning that the conclusions differ from one model to the other.     

认股权证的保险精算定价

引入Mogens Bladt和Tina Hviid Rydberg在无市场假设下关于期权定价的保险精算方法,利用公平保费原则和价格过程的实际概率测度,建立认股权证的定价模型,并给出定价公式.当投资者对原生资产期望回报率为无风险利率时,该定价为风险中性价格.     

农作物单产的最大熵分布及在费率厘定上的应用

农作物单产分布的确定是农业保险中费率厘定的基础。本文引入最大熵原理,基于最大熵优化模型得出农作物单产的最大熵分布,并以此进行费率厘定。同时以辽宁省主要作物水稻、玉米、大豆和花生为例,确定了该四种农作物的费率,分别为4.45%、6.77%、6.34%、6.43%。结果表明:利用最大熵分布理论进行费率厘定不需要事先假定农作物单产分布的形式,而且考虑了更多作物单产分布的信息,为农业保险费率的合理精算提供一种新的可供选择的方法,有助于农业风险决策的科学化。     

中国利率风险溢酬:时变特征与影响因素

利率风险溢酬是长期利率的组成部分,解读它所包含的信息、寻找它的来源有着重要的经济意义。本文先使用利率仿射模型,计算出先验的中国国债利率期限溢酬,然后构建VECM模型,运用脉冲响应、方差分析等技术,分析国债利率的风险溢酬和主要宏观经济变量的动态关系,发现宏观变量对溢酬的影响在当期和滞后几期有明显差异,CPI和GDP是影响最大的两个因素,但信贷供应量和M1的作用也较大。我们同时也发现银行间市场投资者比交易所市场投资者更易受到宏观经济的影响。