The Convergence of Set-Valued Scenario Approach for Downside Risk Minimization

Scenario approach is a widely used tool in portfolio risk management,however,it often runs into dilemma when determining the distribution of asset returns with insufficient information,which will be used to simulate the scenarios.Also the quality of generated scenarios are not guaranteed even when the distribution of asset returns is known exactly.A set-valued scenario approach was proposed by Zhu,et al.(2015)as a possible remedy.As a necessary supplement of the results proposed by Zhu,et al.(2015),this paper theoretically investigates the convergent property of the numerical solution based on the set-valued scenario approach under the condition that the underlying distribution is known.

Solving Markov Decision Processes with Downside Risk Adjustment

Markov decision processes （MDPs） and their variants are widely studied in the theory of controls for stochastic discrete- event systems driven by Markov chains. Much of the literature focusses on the risk-neutral criterion in which the expected rewards, either average or discounted, are maximized. There exists some literature on MDPs that takes risks into account. Much of this addresses the exponential utility （EU） function and mechanisms to penalize different forms of variance of the rewards. EU functions have some numerical deficiencies, while variance measures variability both above and below the mean rewards; the variability above mean rewards is usually beneficial and should not be penalized/avoided. As such, risk metrics that account for pre-specified targets （thresholds） for rewards have been considered in the literature, where the goal is to penalize the risks of revenues falling below those targets. Existing work on MDPs that takes targets into account seeks to minimize risks of this nature. Minimizing risks can lead to poor solutions where the risk is zero or near zero, but the average rewards are also rather low. In this paper, hence, we study a risk-averse criterion, in particular the so-called downside risk, which equals the probability of the revenues falling below a given target, where, in contrast to minimizing such risks, we only reduce this risk at the cost of slightly lowered average rewards. A solution where the risk is low and the average reward is quite high, although not at its maximum attainable value, is very attractive in practice. To be more specific, in our formulation, the objective function is the expected value of the rewards minus a scalar times the downside risk. In this setting, we analyze the infinite horizon MDP, the finite horizon MDP, and the infinite horizon semi-MDP （SMDP）. We develop dynamic programming and reinforcement learning algorithms for the finite and infinite horizon. The algorithms are tested in numerical studies and show encouraging performance.

Downside risk and defaultable bond returns

This paper analyzes the influence of downside risk on defaultable bond returns.By introducing a defaultable bond-trading model,we show that the decline in market risk tolerance and information accuracy leads to trading loss under downside conditions.Our empirical analysis indicates that downside risk can explain a large proportion of the variation in yield spreads and contains almost all valid information on liquidity risk.As the credit level decreases,the explanatory power of downside risk increases significantly.We also investigate the predictive power of downside risk in cross-sectional defaultable bond excess returns using a portfolio-level analysis and Fama-Mac Beth regressions.We find that downside risk is a strong and robust predictor for future bond returns.In addition,due to the higher proportion of abnormal transactions in the Chinese bond market,downside risk proxy semi-variance can better explain yield spreads and predict portfolio excess returns than the proxy value at risk.

投资风险度量模式的发展及其比较

文章根据50年代以来各种风险度量模式的发展状况,分析比较了被广泛认可的三种度量模式,即均值-方差模式、Downside-Risk模式和ValueatRisk模式的优劣。

OPTIMAL OPERATIONAL DECISIONS WHEN A MANUFACTURER OFFERS TRADE CREDIT TO HIS RETAILER

In this paper, we develop models to determine operational and financial decisions of a supply chain under the condition that the retailer faces a financial constraint and the manufacturer can offer trade credit to assist the retailer. We first study the case where the retailer is risk-neutral, and derive the optimal ordering and financial decisions. Then, the case where the retailer is risk-averse （downside risk） is studied and-the effects of the risk on the retailer and manufacturer＇s operational and financial decisions are discussed. Finally, numerical examples are provided to conduct managerial analysis.