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Clewlow and Carverhill (1994) developed the general approach of using hedges (Greeks) as control variates. Because the payoff of a hedged portfolio has a lower standard deviation than the payoff of an unhedged one, using delta and gamma hedges can reduce the volatility of the value of the portfolio. Consider the case of writing a European call option with maturity T. We can replicate the payoff by selling the option, investing the premium in a savings account, and rebalancing the holding in the asset at discrete interval times ti =1, . . . , N, with resultant cash ows placed into and out of the savings account (when selling and buying shares, respectively) so as to maintain a self- nancing portfolio.15 A delta hedge consists of holding = C/ S shares in the underlying asset, which is rebalanced at the discrete time intervals. While the hedge is not perfect due to discrete rebalancing, it is quite good with frequent rebalancing. At time T, the hedge consists of the savings account and the asset, which closely replicates the payoff of the option. This can be expressed as N Ct Ct i 1 i C t 0 e r( T t 0 ) St i e r( T t i ) = CT + S i = 0 S

of action of this compound, a time-of-addition study was performed, where the point in viral replication inhibited by 102 was compared with the inhibitors acting at attachment (Chicago Sky Blue) or reverse transcription (AZT47 and nevirapine48). This study indicated that 102 acts at a point in the virus life cycle immediately after the target for the RTIs AZT and nevirapine. Additional mechanism of action studies are ongoing, and preliminary data suggest that 102 inhibits the production of double-stranded viral DNA from the single-stranded DNA intermediate, in contrast to traditional RT inhibitors that block the generation of single-stranded DNA from the RNA template.39 Low water solubility, less potency against drug-resistant HIV strains, and fast metabolism are three main obstacles that limit the development of DCK analogs. Additional analog design is likely to use DCP as a new lead to increase the potency against drug-resistant viral strains and improve water solubility and pharmacological properties.

When needing to make sense of a large set of data, the data can be broken down into smaller groups of observations that share something in common Knowing the contents of these smaller groups helps in understanding the entire data set Clustering is a widely used and exible approach to analyzing data, in which observations are automatically organized into groups Those observations within a particular group are more similar to each other than to observations in other groups This approach has been successfully utilized in a variety of scienti c and commercial applications, including medical diagnosis, insurance underwriting, nancial portfolio management, organizing search results, and marketing For example, clustering has been used by retail organizations to analyze customer data based on historical purchases, along with information about the customer, such as their age or where they live.

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Customers are grouped using clustering approaches, and speci c marketing campaigns are then formulated based on the identi ed market segments A data set of animals will be used to illustrate clustering Table 31 describes a series of animal observations (taken from http://archiveicsuciedu/ml/datasets/ Zoo; Murphy and Aha, 1994) Each animal is characterized by a number of variables, including several binary variables, such as whether the animal has hair (hair) or produces milk (milk) The data set also includes a count of the number of animal legs (legs) Cluster analysis organizes the data into groups of similar animals Using the numeric variables shown in Table 31, the data set can be clustered in a number of ways Figure 31 shows one possible grouping of this data A description of how this particular set was clustered will be discussed later in the chapter In Fig 3.

1 the animals have been organized into four groups representing the following general categories: (1) mammals, (2) sh and amphibians, (3) invertebrates, and (4) birds Each group represents a series of similar animals, with the mammals group primarily representing a group of four-legged animals that produce milk, the sh and amphibians group primarily representing a group of aquatic animals, the invertebrates group primarily representing a set of six-legged animals with no backbone, and the birds group primarily representing a set of two-legged airborne animals with feathers Based on an initial inspection of the clusters, the grouping may not appear to adequately represent the different types of animals For example, in Fig 31, an.