Optimal reinsurance under general law-invariant risk measures

In recent years, general risk measures play an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance decision problems using risk measures beyond the classical expected utility framework. In this paper, we first show that the stop-loss reinsurance is an optimal contract under law-invariant convex risk measures via a new simple geometric argument. A similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution. These two results highlight that law-invariant convex risk measure is better and more robust, in the sense that the corresponding optimal reinsurance still provides the protection coverage against extreme loss irrespective to the potential increment of its probability of occurrence, to expected larger claim than Value at Risk and Conditional Tail Expectation which are more commonly used. Several illustrative examples will be provided.     

On Mixed and Compound Mixed Poisson Distributions

Recursive formulae are derived for the evaluation of the t-th order cumulative distribution function and the t-th order tail probability of compound mixed Poisson distributions in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. Also, some general results are derived for the evaluation of the t-th order moments of stop-loss transforms. The recursions can be applied for the exact evaluation of the probability function, distribution function, tail probability and stop-loss premium of compound mixed Poisson distributions and the corresponding mixed Poisson distributions. Several examples are also presented.     

General convex order on risk aggregation

Using a general notion of convex order, we derive general lower bounds for risk measures of aggregated positions under dependence uncertainty, and this in arbitrary dimensions and for heterogeneous models. We also prove sharpness of the bounds obtained when each marginal distribution has a decreasing density. The main result answers a long-standing open question and yields an insight in optimal dependence structures. A numerical algorithm provides bounds for quantities of interest in risk management. Furthermore, our numerical results suggest that the bounds obtained in this paper are generally sharp for a broader class of models.     

A note on generalized distortion risk measures

A generalized distortion risk measure is introduced as power of the mean absolute deviation power of a distorted random variable with respect to a location parameter. This class of risk measures extends both the distortion risk measure by Wang and Denneberg and the class of financial risk measures by Pedersen and Satchell, which itself contains the class of Stone. Integral representations and a stop–loss order preserving property of a special up-side risk measure are derived.     

Stochastic orders in dynamic reinsurance markets

We consider a dynamic reinsurance market, where the traded risk process is driven by a compound Poisson process and where claim amounts are unbounded. These markets are known to be incomplete, and there are typically infinitely many martingale measures. In this case, no-arbitrage pricing theory can typically only provide wide bounds on prices of reinsurance claims. Optimal martingale measures such as the minimal martingale measure and the minimal entropy martingale measure are determined, and some comparison results for prices under different martingale measures are provided. This leads to a simple stochastic ordering result for the optimal martingale measures. Moreover, these optimal martingale measures are compared with other martingale measures that have been suggested in the literature on dynamic reinsurance markets.Received: March 2004, Mathematics Subject Classification (2000): 62P05, 60J75, 60G44JEL Classification: G10     

A Portfolio's Country Exposure Management: The Case of Latin American Mutual Funds

This study empirically examines the forecasting ability and performance of Latin American fund managers by evaluating changes in portfolio country exposure. It employs a methodology based on attribution returns. An attribution return is defined as the difference between the actual monthly fund return and the return that would have been generated by the previous month portfolio's country exposure. The study finds three major results. In the aggregate, Latin American fund managers demonstrate forecasting ability as evidenced by a positive and statistically significant attribution return. The fund managers outperform a regional benchmark when measured with Jensen's alpha, and the attribution return is positively correlated with alpha. Attribution returns are mostly negative during periods of financial instability in the region.     

Does sustainable investing reduce portfolio risk? A multilevel analysis

This study complements and extends prior research on the risk mitigation role of sustainable investing. We use a continuous measure of funds' sustainability traits, rather than a categorical approach, and assess impact on risk directly rather than by looking at fund performance in up versus down markets. We find that sustainable investing plays a significant role in mitigating total, systematic, and idiosyncratic risk of equity funds, even after controlling for other fund characteristics. Further evidence indicates that the explanation for the risk reduction role of sustainable funds largely runs through traits of the firms held in the funds.     

Vector-valued coherent risk measures

We define (d,n)-coherent risk measures as set-valued maps from into satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the passage from valued random portfolio to valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.Received: February 2004, Mathematics Subject Classification (2000): 91B30, 46E30JEL Classification: D81, G31     

Spectral Risk Measures: Properties and Limitations

Spectral risk measures (SRMs) are risk measures that take account of user risk-aversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative approaches based on exponential and power utility functions. A number of problems are identified with both types of spectral risk measure. The general lesson is that users of spectral risk measures must be careful to select utility functions that fit the features of the particular problems they are dealing with, and should be especially careful when using power SRMs.

偏度风险溢酬及其预测能力研究——基于人民币对外汇期权的实证分析

基于无模型方法,利用在岸人民币对美元期权的市场价格数据,通过提取风险中性三阶矩和已实现三阶矩估算偏度风险溢酬,并考察其时变特征、与波动率风险溢酬的关系和对汇率尾部风险的预测能力。结果表明,外汇期权市场上存在显著为负的时变偏度风险溢酬;偏度风险溢酬与波动率风险溢酬存在共同的驱动因子。此外,偏度风险溢酬在短期内对汇率暴涨的尾部风险事件具备一定的预测能力。当偏度风险溢酬增加时,投资者对偏度风险的厌恶加剧,预期未来人民币大幅贬值的概率上升。