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.

The Downside Of Openness

The opening of China’s financial markets may not be the key to resolving the U.S. trade deficit As an investment banker, Henry Paulson was known for his 70-odd visits to China. Thishigh frequency has been sustained since he took over the U.S.

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。

VaR方法与资产组合分析

本文针对风险方差度量方法投资收益正态分布假设的缺陷,引入了考察投资绩效对资产组合影响的VaR方法,在探讨VaR定义以及计算方法的基础上,求解了VaR约束下的资产组合问题。在VaR框架下,建立了形同于Sharpe指数的单位风险超额收益指数,并提出了类似于均值—方差分析中存在无风险资产的两基金分离定理,从而弥补了方差度量方法的不足,提高了资产配置模型的应用效率。