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We know intuitively that high-risk ventures should yield a risk premium and thus higher returns. In 1 we even quanti ed risk in terms of a standard deviation s of a probability distribution of returns. What we want to do in this chapter is to go one step further to answer the question How much more should I get for taking additional risk We will answer this question according to traditional methods, and point to places that these methods can be improved or, in some cases, where these methods have already been improved but the improvement has not been widely implemented. Standard deviation is a valuable concept for modeling volatility of stock returns, but the estimated standard deviations often seem foreign to an investor and not easily transferred to the bottom line: the price. Since business managers and bankers think of risk in terms of dollars of loss, standard deviation does not t very well into the language of business. It is not necessarily true that the higher the risk as measured by s, the higher are the losses. The senior management needs a number that gives the worst-case scenario of dollar loss, in a prescribed holding period. Enter value at risk (VaR). VaR puts a dollar amount on the highest expected loss on an investment. VaR has become popular since the US nancial giant J.P. Morgan published RiskMetricsTM methods in 1995. We will provide an overview of VaR in this chapter and many extensions that have been developed. For further details see surveys of VaR by Duffe and Pan (1997) and Jorion (1997). Some issues involving the time horizon for VaR need

(1999) Global patterns of plant invasions and the concept of invasibility Ecology 80, 1522 36 Lotka, AJ (1925) Elements of Physical Biology Williams and Wilkins, Baltimore, MD Reprinted 1956, Dover Publications, New York Lotka, AJ (1927) Fluctuations in the abundance of species considered mathematically (with comment by V Volterra) Nature 119, 12 13 Mace, GM and Lande, R (1991) Assessing extinction threats: towards a re-evaluation of IUCN threatened species categories Conservation Biology 5, 148 57 Magallon, S and Sanderson, MJ (2001) Absolute diversi cation rates in angiosperm clades Evolution 55, 1762 80 Manly, BJ (1990) Stage-Structured Populations Sampling, Analysis and Simulation Chapman and Hall, London Martinez, ND, Hawkins, BA, Dawah, HA and Feifarek, BP (1999) Effects of sampling effort on characterization of food-web structure Ecology 80, 1044 55 May, RM.

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Social Media De ned 319 Social Media Marketing Basics 320 Measuring Social Media Activities and Campaigns 323 Putting together a keyword list 323 Finding relevant conversations online 323 Quantifying buzz with keyword trends 324 Understanding content and sentiment 325 Analyzing Site Traf c from Social Media 326 Business value measures 331 Measuring Social Media Tools on Your Site 332 Tracking comments 332 Tracking subscriptions 335 Tracking content-sharing tools 337 Tracking Social Media at Lollapaloozacom 340.

Challenges include the lack of a global Network Context; the need to minimize overhead required for coordination across nodes; limited decision times; possible lossy communications; and so on To address these challenges, an anytime coordination approach can be used that builds upon three recent advances: (i) factored MDPs, a unique approach for solving large-scale MDPs that exploits problem structure; (ii) coordination graphs, a distributed coordination algorithm that allows multiple nodes to ef ciently nd the optimal action setting through neighborhood communication; and (iii) distributed inference for coordinated decision-making The impact of the communication required for coordination on the available resources is also incorporated This effect can be evaluated by combining the models with the predictive approach developed for the Network Context Manager Using estimates, the level of coordination can be traded against the bandwidth required to achieve this coordination.

(1972) Will a large complex system be stable Nature 238, 413 14 May, RM (1973a) Stability and Complexity in Model Ecosystems Princeton University Press, Princeton, NJ May, RM (1973b) On relationships among various types of population model American Naturalist 107, 46 57 May, RM (1976) Simple mathematical models with very complicated dynamics Nature 261, 459 67 May, RM (1978) Host-parasitoid systems in patchy environments, a phenomenological model Journal of Animal Ecology 47, 833 43 May, RM (1981) Theoretical Ecology Principles and Applications Blackwell Science, Oxford May, RM (1984) An overview: real and apparent patterns in community structure In: Ecological Communities: Conceptual Issues and the Evidence (DR Strong, D Simberloff, CG Abele and AB Thistle, eds), pp 3 18 Princeton University Press, Princeton, NJ May, RM and Oster, GF (1976) Bifurcations and dynamic complexity in simple ecological models.

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