On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

Approximate solutions to stochastic dynamic programs

This paper examines the properties of various approximation methods for solving stochastic dynamic programs in structural estimation problems. The problem addressed is evaluating the expected value of the maximum of available choices. The paper shows that approximating this by the maximum of expected values frequently has poor properties. It also shows that choosing a convenient distributional assumptions for the errors and then solving exactly conditional on the distributional assumption leads to small approximation errors even if the distribution is misspecified. © 1997 Cambridge University Press.

Predicting stock market returns and volatility with investor sentiment : evidence from eight developed countries

We test the predictive ability of investor sentiment on the return and volatility at the aggregate market level in the U.S., four largest European countries and three Asia-Pacific countries. We find that in the U.S., France and Italy periods of high consumer confidence levels are followed by low market returns. In Japan both the level and the change in consumer confidence boost the market return in the next month. Further, shifts in sentiment significantly move conditional volatility in most of the countries, and in Italy such impacts lead to an increase in returns by 4.7% in the next month.

Asymptotic minimax robust and misspecified Lorden quickest change detection for dependent stochastic processes

The quick detection of an abrupt unknown change in the conditional distribution of a dependent stochastic process has numerous applications. In this paper, we pose a minimax robust quickest change detection problem for cases where there is uncertainty about the post-change conditional distribution. Our minimax robust formulation is based on the popular Lorden criteria of optimal quickest change detection. Under a condition on the set of possible post-change distributions, we show that the widely known cumulative sum (CUSUM) rule is asymptotically minimax robust under our Lorden minimax robust formulation as a false alarm constraint becomes more strict. We also establish general asymptotic bounds on the detection delay of misspecified CUSUM rules (i.e. CUSUM rules that are designed with post- change distributions that differ from those of the observed sequence). We exploit these bounds to compare the delay performance of asymptotically minimax robust, asymptotically optimal, and other misspecified CUSUM rules. In simulation examples, we illustrate that asymptotically minimax robust CUSUM rules can provide better detection delay performance at greatly reduced computation effort compared to competing generalised likelihood ratio procedures.

Enhanced stochastic mobility prediction with multi-output Gaussian processes

Outdoor robots such as planetary rovers must be able to navigate safely and reliably in order to successfully perform missions in remote or hostile environments. Mobility prediction is critical to achieving this goal due to the inherent control uncertainty faced by robots traversing natural terrain. We propose a novel algorithm for stochastic mobility prediction based on multi-output Gaussian process regression. Our algorithm considers the correlation between heading and distance uncertainty and provides a predictive model that can easily be exploited by motion planning algorithms. We evaluate our method experimentally and report results from over 30 trials in a Mars-analogue environment that demonstrate the effectiveness of our method and illustrate the importance of mobility prediction in navigating challenging terrain.

Correlations and volatility spillovers across commodity and stock markets: Linking energies, food, and gold

This paper employs a VAR-GARCH model to investigate the return links and volatility transmission between the S&P 500 and commodity price indices for energy, food, gold and beverages over the turbulent period from 2000 to 2011. Understanding the price behavior of commodity prices and the volatility transmission mechanism between these markets and the stock exchanges are crucial for each participant, including governments, traders, portfolio managers, consumers, and producers. For return and volatility spillover, the results show significant transmission among the S&P 500 and commodity markets. The past shocks and volatility of the S&P 500 strongly influenced the oil and gold markets. This study finds that the highest conditional correlations are between the S&P 500 and gold index and the S&P 500 and WTI index. We also analyze the optimal weights and hedge ratios for commodities/S&P 500 portfolio holdings using the estimates for each index. Overall, our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity and commodity markets. © 2013 Elsevier B.V.

The impacts of exchange rate volatility on vegetable trade flows

Trade flows of commodities are generally affected by the principles of comparative advantage in a free trade. However, trade flows might be enhanced or distorted not only by various government interventions, but also by exchange rate fluctuations among others. This study applies a commodity-specific gravity model to selected vegetable trade flows among Organization for Economic Co-operation and Development (OECD) countries to determine the effects of exchange rate uncertainty on the trade flows. Using the data from 1996 to 2002, the results show that, while the exchange rate uncertainty significantly reduces trade in the majority of commodity flows, there is evidence that both short- and long-term volatility have positive effect on trade flows of specific commodities. This study also tests the regional preferential trade agreements such as the North American Free Trade Agreement (NAFTA), the Asia-Pacific Economic Cooperation (APEC) and the EU, and their different effects on commodities.

Learned stochastic mobility prediction for planning with control uncertainty on unstructured terrain

Motion planning for planetary rovers must consider control uncertainty in order to maintain the safety of the platform during navigation. Modelling such control uncertainty is difficult due to the complex interaction between the platform and its environment. In this paper, we propose a motion planning approach whereby the outcome of control actions is learned from experience and represented statistically using a Gaussian process regression model. This mobility prediction model is trained using sample executions of motion primitives on representative terrain, and predicts the future outcome of control actions on similar terrain. Using Gaussian process regression allows us to exploit its inherent measure of prediction uncertainty in planning. We integrate mobility prediction into a Markov decision process framework and use dynamic programming to construct a control policy for navigation to a goal region in a terrain map built using an on-board depth sensor. We consider both rigid terrain, consisting of uneven ground, small rocks, and non-traversable rocks, and also deformable terrain. We introduce two methods for training the mobility prediction model from either proprioceptive or exteroceptive observations, and report results from nearly 300 experimental trials using a planetary rover platform in a Mars-analogue environment. Our results validate the approach and demonstrate the value of planning under uncertainty for safe and reliable navigation.