TVaR-based capital allocation with copulas

Because of regulation projects from control organisations such as the European solvency II reform and recent economic events, insurance companies need to consolidate their capital reserve with coherent amounts allocated to the whole company and to each line of business. The present study considers an insurance portfolio consisting of several lines of risk which are linked by a copula and aims to evaluate not only the capital allocation for the overall portfolio but also the contribution of each risk over their aggregation. We use the tail value at risk (TVaR) as risk measure. The handy form of the FGM copula permits an exact expression for the TVaR of the sum of the risks and for the TVaR-based allocations when claim amounts are exponentially distributed and distributed as a mixture of exponentials. We first examine the bivariate model and then the multivariate case. We also show how to approximate the TVaR of the aggregate risk and the contribution of each risk when using any copula.     

Option pricing when the regime-switching risk is priced

We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two- stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.     

Risk preference modeling with conditional average: an application to portfolio optimization

The paper introduces a new risk measure called Conditional Average (CAVG), which was designed to cover typical attitudes towards risk for any type of distribution. It can be viewed as a generalization of Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), two commonly used risk measures. The preference structure induced by CAVG has the interpretation in Yaari’s dual theory of choice under risk and relates to Tversky and Kahneman’s cumulative prospect theory. The measure is based on the new stochastic ordering called dual prospect stochastic dominance, which can be considered as a dual stochastic ordering to recently developed prospect stochastic dominance. In general, CAVG translates into a nonconvex quadratic programming problem, but in the case of a finite probability space it can also be expressed as a mixed-integer program. The paper also presents the results of computational studies designed to assess the preference modeling capabilities of the measure. The experimental analysis was performed on the asset allocation problem built on historical values of S&P 500 sub-industry indexes. The research was supported by the grant PBZ-KBN-016/P03/99 from the State Committee for Scientific Research.     

DROUGHT RESILIENCE IN AGRICULTURE: THE ROLE OF TECHNOLOGICAL OPTIONS,LAND USE DYNAMICS,AND RISK PERCEPTION

Abstract Sustained droughts coupled with increasing pressure from urbanization severely test the ability of farmers to continue in agriculture. Understanding farmers' resilience to such pressures is increasingly becoming a significant policy concern. In this paper, a new measure of resilience to severe and sustained droughts in agriculture is derived as the ability to continue farming by saving and carrying forward water through the adoption of water efficient technology. In addition, the role of behavioral factors—such as subjective risk perception over the probability of droughts, of the probability of land getting urbanized, and of resistance to revising beliefs over water scarcity situation—in determining farmers' resilience to droughts is explored. Findings highlight the key role played by behavioral factors in influencing the decision to adopt when the economic factors, such as the price of water, do not capture the true opportunity costs of water. The range of available technological options is found to be crucial too, as marginal improvements in technology do not encourage adoption. An empirical application to the case of lettuce farming in Western Australia reveals that in the presence of speculative benefits from land rezoning, technological adoption is done only for enhancing profits in agriculture and not for improving resilience to droughts. Land rezoning possibilities may further distort technology adoption decisions, thereby, reducing resilience to droughts.     

基于模糊理论的机动车辆风险评估

对机动车辆风险进行评估是车险费率厘定的一个重要环节.提出一种基于模糊理论的机动车辆风险评估方法(The Risk Assess of Motor Vehicle Based on Fuzzy Theory,简称RMFT),应用表明该方法在风险评估的精度上取得较好效果.     

中国住房抵押贷款信用风险:理论分析与实证研究

住房抵押贷款为中国经济的持续增长增添了新的动力,随着规模扩大,其信用风险问题已经引起金融机构、政府部门及学者的关注.在分析中国房地产市场特点的基础上研究了适应中国住房抵押贷款违约的理论以及影响住房抵押贷款违约的因素,并通过采集大连市的数据进行了实证分析,首次运用实际数据来比选适应中国市场的理论模型.我们的研究发现:在中国住房抵押贷款市场上,贷款违约的还款能力理论较之于期权理论有着更好的适应性;利率、LTV、偿债比与户籍是影响住房抵押贷款违约的主要因素;也得出另外几个不同于理论假说的结论:家庭收入对借款人违约的影响力不明显,购买二手住房的借款人的违约概率要比新房高.     

一类Sparre Andersen风险模型的Gerber-Shiu函数

本文考虑了一类相邻两次索赔的时间间隔服从Erlang($n$)和Erlang($m$)的混合分布的Sparre Andersen风险模型.主要目的是研究Gerber-Shiu函数$\phi_\delta(u)$,首先证明了$\phi_\delta(u)$满足一个高阶的积分微分方程,然后讨论了广义Lundberg方程根的性质,在此基础上导出了$\phi_\delta(u)$的拉普拉斯变换并且证明了$\phi_\delta(u)$满足一个更新方程,最后给出了一个例子.     

Ruin probability for correlated negative risk sums model with Erlang processes

This paper studies a Sparre Andersen negative risk sums model in which the distribution of ＂interclaim＂ time is that of a sum of n independent exponential random variables. Thus, the Erlang（n） model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ（u） are given. For some special cases a closed-form expression for ψ（u） is derived.     

银行信用风险演变的KMV模型分析—以五家中小商业银行为例

利用KMV模型方法,借助预期违约概率（EDF）和违约距离（DD）两个指标分析在我国A股上市的五家中小商业银行的信用风险。着重分析其预期违约概率的变化以及违约距离对股票价格、无风险利率、股权价值波动率等参数的敏感性。结果表明：五家商业银行在2008年前10个月的EDF上升明显,2008年11月EDF开始明显回落。从宁波银行的个案来看,违约距离对无风险利率的敏感性较弱、对股价在较低价位时的敏感性较强,而在较高价位时敏感性较弱,对股权价值波动率的敏感性较强。从违约距离对各参数的敏感性分析结论出发,阐述了稳定并提振我国A股股市的重要性。     

Mean‐variance hedging with basis risk

Basis risk arises in a number of financial and insurance risk management problems when the hedging assets do not perfectly match the underlying asset in a hedging program. Notable examples in insurance include the hedging for longevity risks, weather index–based insurance products, variable annuities, etc. In the presence of basis risk, a perfect hedging is impossible, and in this paper, we adopt a mean‐variance criterion to strike a balance between the expected hedging error and its variability. Under a time‐dependent diffusion model setup, explicit optimal solutions are derived for the hedging target being either a European option or a forward contract. The solutions are obtained by a delicate application of the linear quadratic control theory, the method of backward stochastic differential equation, and Malliavin calculus. A numerical example is presented to illustrate our theoretical results and their interesting implications.