Optimal hedging when the underlying asset follows a regime-switching Markov process

We develop a flexible discrete-time hedging methodology that minimizes the expected value of any desired penalty function of the hedging error within a general regime-switching framework. A numerical algorithm based on backward recursion allows for the sequential construction of an optimal hedging strategy. Numerical experiments comparing this and other methodologies show a relative expected penalty reduction ranging between 0.9%$0.9\%$ and 12.6%$12.6\%$ with respect to the best benchmark.     

Longevity risk,cost of capital and hedging for life insurers under Solvency II

The cost of capital is an important factor determining the premiums charged by life insurers issuing life annuities. This capital cost can be reduced by hedging longevity risk with longevity swaps, a form of reinsurance. We assess the costs of longevity risk management using indemnity based longevity swaps compared to costs of holding capital under Solvency II. We show that, using a reasonable market price of longevity risk, the market cost of hedging longevity risk for earlier ages is lower than the cost of capital required under Solvency II. Longevity swaps covering higher ages, around 90 and above, have higher market hedging costs than the saving in the cost of regulatory capital. The Solvency II capital regulations for longevity risk generates an incentive for life insurers to hold longevity tail risk on their own balance sheets, rather than transferring this to the reinsurance or the capital markets. This aspect of the Solvency II capital requirements is not well understood and raises important policy issues for the management of longevity risk.     

Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?

Vernic (2006), Bolancé et al. (2008), and Eling (2012) identify the skew-normal and skew-student as promising models for describing actuarial loss data. In this paper, we change the focus from the liability to the asset side and ask whether these distributions are also useful for analyzing the investment returns of insurance companies. To answer this question, we fit various parametric distributions to capital market data which has been used to describe the investment set of insurance companies. Our results show that the skew-student is an especially promising distribution for modeling asset returns such as those of stocks, bonds, money market instruments, and hedge funds. Combining the results of Vernic (2006), Bolancé et al. (2008), Eling (2012), and this paper, it appears that the skew-student is a promising actuarial tool since it describes both sides of the insurer’s balance sheet reasonably well.     

Second order risk aggregation with the Bernstein copula

We analyze the tail of the sum of two random variables when the dependence structure is driven by the Bernstein family of copulas. We consider exponential and Pareto distributions as marginals. We show that the first term in the asymptotic behavior of the sum is not driven by the dependence structure when a Pareto random variable is involved. Consequences on the Value-at-Risk are derived and examples are discussed.     

The loss given default of a low-default portfolio with weak contagion

In this paper we study the loss given default (LGD) of a low default portfolio (LDP), assuming that there is weak credit contagion among the obligors. We characterize the credit contagion by a Sarmanov dependence structure of the risk factors that drive the obligors’ default, where the risk factors are assumed to be heavy tailed. From a new perspective of asymptotic analysis, we derive a limiting distribution for the LGD. As a consequence, an approximation for the entire distribution, in contrast to just the tail behavior, of the LGD is obtained. We show numerical examples to demonstrate the limiting distribution. We also discuss possible applications of the limiting distribution to the calculation of moments and the Value at Risk (VaR) of the LGD.     

COPD急性加重合并活动性肺结核患者的危险因素及临床特征分析

目的分析慢性阻塞性肺疾病（COPD）急性加重合并活动性肺结核患者的危险因素及临床特征,以指导临床治疗。方法选取COPD急性发作合并活动性肺结核患者42例（合并组）及同期单纯COPD急性发作的患者72例（对照组）,比较两组患者的临床特征,并采用单因素分析及logistic回归分析其危险因素。结果两组患者的部分临床特征有统计学差异（均P＜0.05）。单因素分析表明,吸烟史、营养不良、长期吸入糖皮质激素史及既往有肺结核史是COPD急性发作合并活动性肺结核的主要危险因素（均P＜0.05）。多因素分析发现,营养不良（OR=4.100,95%CI：1.471～11.431）、长期吸入糖皮质激素史（OR=2.695,95%CI：1.078～6.739）及既往肺结核史（OR=11.102,95%CI：3.076～40.065）为独立危险因素（均P＜0.05）。结论根据危险因素早期识别合并活动性肺结核的高危COPD患者,可尽早明确诊断,给予积极治疗。     

Exact capacities and star-shaped distorted probabilities

We are interested in capacities which are deformations of probability, i.e. v=fP. We characterize balanced, totally balanced, and exact capacities by properties concerning the probability transformation function, f. These results allow us to obtain simple new characterizations of a large pattern of risk aversions relevant to Yaari’s dual theory of choice under risk.     

Epistemic Risk and Relativism

It is generally assumed that there are (at least) two fundamental epistemic goals: believing truths, and avoiding the acceptance of falsehoods. As has been often noted, these goals are in conflict with one another. Moreover, the norms governing rational belief that we should derive from these two goals depend on how we weight them relative to one another. However, it is not obvious that there is one objectively correct weighting for everyone in all circumstances. Indeed, as I shall argue, it looks as though there are circumstances in which a range of possible weightings of the two goals are all equally epistemically rational.

What are the actual costs of cyber risk events?

Cyber risks are high on the business agenda of every company, but they are difficult to assess due to the absence of reliable data and thorough analyses. This paper is the first to consider a broad range of cyber risk events and actual cost data. For this purpose, we identify cyber losses from an operational risk database and analyze these with methods from statistics and actuarial science. We use the peaks-over-threshold method from extreme value theory to identify “cyber risks of daily life” and “extreme cyber risks”. Human behavior is the main source of cyber risk and cyber risks are very different compared with other risk categories. Our models can be used to yield consistent risk estimates, depending on country, industry, size, and other variables. The findings of the paper are also useful for practitioners, policymakers and regulators in improving the understanding of this new type of risk.     

Asymptotic Results for Tail Probabilities of Sums of Dependent and Heavy-Tailed Random Variables

Abstract Let X1,X2,...be a sequence of dependent and heavy-tailed random variables with distributions F1,F2,…. on (-∞,∞),and let т be a nonnegative integer-valued random variable independent of the seq...