# An ExampleSample Clauses

An Example. Consider a company whose stock price is S0 = 90 today. Suppose tomorrow, with proba- bility 0.9 the stock price is S1 = 100 and with probability 0.1 the stock price is S1 = 80. Also suppose that the interest rate r = 0. Consider a contract that will deliver a share of S to the holder tomorrow, but the payment has to be made today. This is an example of a forward contract with strike price 0. What is the price of such a contract?−An intuitive answer is that since E(S1) = (.9)100+(.1)80 = 98 and r = 0, the price for the contract is 98 dollars. However this answer is incorrect. Let us recall that the price of a general forward contract with strike K is S0 Ke−rT . Since K = 0 the price is S0 = 90. We show in (2.3.3) that 90 dollars is the no-arbitrage price of the forward contract with K = 0. Hence if the contract is priced at 98 dollars, there will be an arbitrage opportunity. Indeed we would simply sell such a contract at 98 dollars, and use the money to buy one share of stock at 90. Tomorrow we give the share of stock to the contract holder to close our position, and make an 8 dollar profit without risk.We want to understand why giving the price by E(S1) is incorrect. Recall from Section (2.2) that pricing by Expectation is an implicit appeal to the Law of Large Number. How- ever, the Law of Large Number does not apply in the current situation. Indeed, observe that in this case we only have one instance of S1. That is there is only one variable S1 that we receive the random payment from. This clearly does not fall into the large number of independent random variables context of the the Law of Large Number. What if we sell the contracts to many buyers to create an instance of a large number of random variables? Unfortunately here the Law of Large Number still does not apply; since all of these buyers will face the same S1. That is every one has to observe the same stock price tomorrow from the same company. We can say there are many identical copies of a random variable; but this does not fulfill the independent requirement of the the Law of Large Number.We remark that there is an approach of pricing financial derivative by taking expecta- tion. However, it is an expectation that is taken under a risk neutral probability, which we have yet defined. We will present this approach in (2.7.3).‌
An Example. The basic formalism we use here are logical implications like p.q => r.t meaning “when p and q hold, then also r and t hold”. This is often called (definite) Horn clauses.16 We use here a notion from AIFω , a novel add-on for OFMC for denoting the implications, while AIFω rules actually mean state transitions. For the formulas we are using in this section, however, it does not make a difference. The full language of AIFω will be explained in a special chapter later.Let us begin with the intruder, and let iknows(m) stand for “the intruder knows m”. We could specify first his initial knowledge like this:=> iknows( a); => iknows( pk( a));=> iknows( b); => iknows( pk( b ));=> iknows( i); => iknows( pk( i)); => iknows( inv( pk( i)));to mean that the intruder knows the agents a, b, i their public keys and his own private key. Here we use implications without a left-hand side, i.e., the right-hand side facts holds unconditionally. If we want to consider more agents, then we would have to make long enumerations. ThereforeAIFω allows to first define some data types:Honest = {a, b}; Dishonest = { i};User = Honest ++ Dishonest;We can then use these types in rules and later change the number of agents without changing any rules and without making long enumerations. To that end, every rule has a rule head of the form rulename(V ariable : Type, V ariable : Type, ...) The type can be any of the user-defined types (like Honest here) or Untyped. Untyped variables, however, have an important restriction: every untyped variable must occur in the left-hand side (and may occur in the right-hand side also). In other words, it is not allow to have untyped variables that only occur in the right-hand side.The listing above is then written simply as follows:users( A: User) => iknows( A); publickeys( A: User) => iknows( pk( A ));privatkeys( D: Dishonest) => iknows( inv( pk( D )));The first rule has the name “users” and says that for any A of type User, the intruder knows A. The other rules are similar.Let now• crypt(k, m) stand for {m}k, i.e., the asymetric encryption with key k of message m,• and pair(m1, m2) stand for the pair of m1 and m2.Then the Dolev-Yao model for asymmetric encryption and pair is described by the following formulas:asymenc( M1 : untyped , M2 : untyped ) iknows( crypt( M1 , M2 )). iknows( inv( M1 )) => iknows( M2 ); asymdec( M1 : untyped , M2 : untyped ) iknows( M1 ). iknows( M2 ) => iknows( crypt( M1 , M2 )); 16Actually, by definition, Horn clauses can on...
An Example. C. Space for sustainability messages Each Licensee will have to decide the actual “Sustainability Message” it wants to use. Here below are examples of the message that can be used:
An Example. Given the decision tree and the guidelines described in sec- tion 2.1., annotating a given item consists in applying a se- ries of tests to a sentence containing the target indefinite, bearing in mind the context in which it appears. Consider one of the items in the annotation task (the target use of any is underlined and in italics):2(2) Item 80: To avoid any presumptions about the struc- ture of the DNA, we replaced the bent DNA in the ac- tual complex with the phosphate backbone for B-form DNA that was used to model the CAP/DNA complex.Applying the first test, [a], leads to the result S-, since it is impossible to continue the sentence containing the target in- definite with an episodic sentence starting with the pronoun they that would refer to “presumptions”. The next test to be applied is therefore [c], the test for universal meaning. The result of applying that test is positive, since from the given context a (rather artificial) scheme For every presumption (about the structure etc.) x: to avoid x we replaced the bent 2For simplicity, we have reduced the amount of context sur- rounding the target indefinite and given only the sentence that con- tains the target. As mentioned at the end of section 2.2., annotators had access to one hundred tokens left and right of the target. Negative polarity Free choice Other20 2018 1816 1614 1412 1210 108 86 64 42 20 0AA AM CA DN Q FC UFC GEN IND IR CO SU UN Q IR SU SK UN Figure 2: Average distribution of functions for any over 5 annotators. The error bars show the standard error. ∀DNA etc. can be inferred. The result + leads to the test [e], the test for anti-additivity, which comes out positive too. [e] requires the annotator to replace the phrase any presump- tions about the structure of the DNA in (2) with a disjunc- tion of two other NPs and check if a conjunction of corre- sponding sentences each containing only one of those NPs follows. For example in this case the sentences in ques- tion would be To avoid problem1 or problem2, we replaced the bent DNA etc. and To avoid problem1, we replaced the bent DNA etc. and to avoid problem2, we replaced etc.. It is clear that the second sentence does indeed follow from the first. The next test to be applied is then [g], the test for negative meaning. Since the target indefinite is not in the immediate scope of sentential negation, we construct a sentence To avoid a presumption or no presumption, we re-Figure 5: Average distribution of functions for some over 5 annota...
An Example. Where will the device be stored when it is not in use? • The kitchen bench, plugged into the charger. Who's responsibility is it to charge the devices? • Child's name goes here. How much time will be spent using the device at home? (Per day / week) • 30mins 3 times per week. When will the device be used at home? • Between 5-6pm only for the permitted time. What will the device be used for during these times? (Games / researching / making moves / taking photos / creative writing etc). • Reading / drawing / researching a set topic / movie making / Mathletics / Reading Eggs. Any other activity must be checked first. Where is the device to be used? • Couch in the family room or at the kitchen table only. What happens if I don't follow the rules with my device? • My device time for the rest of the week or the following week is removed. What happens if I ask to use the device outside of the set times? • Each time I ask, 10 mins is removed from my device time the following week.
An Example. Although this paper is primarily about reason, belief, the passions and motivation, I want to further illustrate the importance of the doctrine of impressions and ideas on these topics with a point about the beginning of Book 3 and the moral sentiments. In the advertisement for Book 3, after claiming that the book ‘is in some measure independentof the other two’, Hume says It must only be observ’d, that I continue to make use of the terms, impressions and ideas, in the same sense as formerly; and that by impressions I mean ourstronger perceptions, such as our sensations, affections and sentiments; and by ideas the fainter perceptions, or the copies of these in the memory and imagination. (T p. 292; SBN 455 facing) The only thing Hume asks his new readers to bring to Book 3 is the distinction and relation between impressions and ideas. He then goes on to structure 3.1.1 in terms of that distinction:this distinction gives rise to a question, with which we shall open up our present enquiry concerning morals, Whether ’tis by means of our ideas or impressions wedistinguish betwixt vice and virtue, and pronounce an action blamable or praiseworthy? This will immediately cut off all loose discourses and declamations, and reduce us to something precise and exact on the present subject. (T 3.1.1.3; SBN 456)It is immediately apparent that ‘[t]hose who affirm that virtue is nothing but a conformity to reason… concur in the opinion, that morality, like truth, is discern’d merely by ideas, and by their juxta-position and comparison’ (T 3.1.1.4; SBN 456). We need to ‘consider, whether it be possible, from reason alone, to distinguish betwixt moral good and evil’.Now if the idea of ‘moral good’ is derived from an impression, the way the idea of ‘natural good’ is derived from an impression of pleasure, we know in advance that it cannot come from reason alone. Reason can never produce an impression or a new idea. Those who have read Book 1 and 2 will see this right away. More discussion is required for others, and Hume proceeds to give it. The ensuing discussion (paragraphs 5-16) also uses earlier material, concerning motivation, and we will get back to that material shortly. Only one possibility remains open to those who would find moral distinctions in reason alone. Although the faculty of reason cannot discover a new idea, it can, roughly speaking, discover a new relation of ideas. Hume argues against this possibility in the (bulk of the) rest of this section, paragraphs...
An Example. Suppose that in our market there are three commodities, say (1) CPU, (2) live memory, and (3) disk, and that the current market prices, in “Grid dollars” (G\$), are G\$3, G\$4, and G\$5 respectively. Suppose further that the current levels ofexcess demand are, again respectively, 1000, -2000, and 0, and that each price increase of G\$1 in each commodity has been measured, at prices near this level, to reduce the demand for this commodity by 500 and increase the supply by 500, giving a decrease of 1000 in excess demand. Finally, suppose that each increase of G\$1 in each commodity results in a decrease of 50 in the demand of each of the other two commodities, resulting from budgetary constraints of the users and also the fact that if, for instance, a user plans to use less CPU, then that user’s need for memory might decrease as well. Note that this constraint reflects the above claim that the excess demand function of each commodity is in fact a function of the entire price vector and not just the price associated to that commodity. We can calculate our updated price as follows: Form the matrix and solve the discretized equation coming from Equation 1 above, which is to give us the approximate values so our new pricing will be G\$2.98, =G\$5.02, G\$4.45.Note that our new prices are approximations of equilibrium prices based on linearizations of the various market sensitivities, which we certainly cannot assume to be linear. Thus we say that our procedure converges to equilibrium prices rather than finding them immediately and precisely.