LECTURE 10: CHANGE OF MEASURE AND THEGIRSANOV THEOREM

Pbendell

Description

• exposé - matière potentielle : that the event hct
• cours magistral
• exposé

LECTURE 10: CHANGE OF MEASURE AND THE GIRSANOV THEOREM 1. Introduction The Cameron-Martin theorem, which has figured prominently in the developments of the last several lectures, is the most important special case of the far more general Girsanov theorem, which is our next topic of discussion. Like the Cameron-Martin theorem, the Girsanov theorem relates the Wiener measure P to different probability measures Q on the space of continuous paths by giving an explicit formula for the likelihood ratios between them.

• sterling investors
• drift term
• pricing barrier options
• exchange rate yt
• girsanov theorem
• change of measure
• likelihood ratio
• probability
• exp
• process

Sujets

• Cours magistral
• Exposé
• Cameron
• Measure
• Process
• Probability
• Theorem
• Exchange
• Pricing
• Sterling

Informations

• Publié par: mochug
• Nombre de lectures: 31
• Langue: English

Extrait

Pinker.qxd 09/29/04 2:54 PM Page 1
Steven Pinker
Why nature & nurture
won’t go away
W hen Richard Mulcaster referred in that debates over nature and nurture
1581 to “that treasure . . . bestowed on evoke more rancor than just about any
them by nature, to be bettered in them issue in the world of ideas.
by nurture,” he gave the world a eupho- During much of the twentieth century,
nious name for an opposition that has a common position in this debate was to
been debated ever since. People’s beliefs deny that human nature existed at all–
about the relative importance of heredi- to aver, with José Ortega y Gasset, that
ty and environment affect their opinions “Man has no nature; what he has is his-
on an astonishing range of topics. Do tory.” The doctrine that the mind is a
adolescents engage in violence because blank slate was not only a cornerstone
of the way their parents treated them of behaviorism in psychology and social
early in life? Are people inherently ag- constructionism in the social sciences,
gressive and sel½sh, calling for a market but also extended widely into main-
1economy and a strong police, or could stream intellectual life.
they become peaceable and cooperative, Part of the blank slate’s appeal came
allowing the state to wither and a spon- from the realization that many differ-
taneous socialism to blossom? Is there a ences among people in different classes
universal aesthetic that allows great art and ethnic groups that formerly were
to transcend time and place, or are peo- 1 Carl N. Degler, In Search of Human Nature:
ple’s tastes determined by their era and The Decline and Revival of Darwinism in American
culture? With so much seemingly at Social Thought (New York: Oxford University
Press, 1991); Steven Pinker, The Blank Slate: stake in so many ½elds, it is no surprise
The Modern Denial of Human Nature (New York:
Viking, 2002); Robin Fox, The Search for Soci-
ety: Quest for a Biosocial Science and Morality
Steven Pinker, Johnstone Family Professor in the (New Brunswick, N.J.: Rutgers University
department of psychology at Harvard University, Press, 1989); Eric M. Gander, On Our Minds:
conducts research on language and cognition. A How Evolutionary Psychology Is Reshaping the
Nature-Versus-Nurture Debate (Baltimore: Fellow of the American Academy since 1998, he
Johns Hopkins University Press, 2003); Johnis the author of six books, including “How the
Tooby and Leda Cosmides, “The Psychological
Mind Works” (1997), “The Language Instinct”
Foundations of Culture,” in The Adapted Mind:
(2000), and “The Blank Slate” (2002). Evolutionary Psychology and the Generation of
Culture, ed. Jerome H. Barkow, Leda Cosmides,
and John Tooby (New York: Oxford University© 2004 by the American Academy of Arts
Press, 1992).& Sciences
Dædalus Fall 2004 1Pinker.qxd 09/29/04 2:54 PM Page 2
Steven thought to reflect innate disparities in that infants have a precocious grasp
Pinker talent or temperament could vanish of objects, intentions, numbers, faces,
on
through immigration, social mobility, tools, and language. Behavioral geneticshuman
nature and cultural change. But another part has shown that temperament emerges
of its appeal was political and moral. If early in life and remains fairly constant
nothing in the mind is innate, then dif- throughout the life span, that much of
ferences among races, sexes, and classes the variation among people within a cul-
can never be innate, making the blank ture comes from differences in genes,
slate the ultimate safeguard against rac- and that in some cases particular genes
ism, sexism, and class prejudice. Also, can be tied to aspects of cognition, lan-
the doctrine ruled out the possibility guage, and personality. Neuroscience
that ignoble traits such as greed, preju- has shown that the genome contains a
dice, and aggression spring from human rich tool kit of growth factors, axon
nature, and thus held out the hope of un- guidance molecules, and cell adhesion
limited social progress. molecules that help structure the brain
Though human nature has been debat- during development, as well as mecha-
ed for as long as people have pondered nisms of plasticity that make learning
their condition, it was inevitable that the possible.
debate would be transformed by the re- These discoveries not only have shown
cent efflorescence of the sciences of that the innate organization of the brain
mind, brain, genes, and evolution. One cannot be ignored, but have also helped
outcome has been to make the doctrine to reframe our very conception of nature
2of the blank slate untenable. No one, and nurture.
of course, can deny the importance of
learning and culture in all aspects of Nature and nurture, of course, are not
human life. But cognitive science has alternatives. Learning itself must be
shown that there must be complex in- accomplished by innate circuitry, and
nate mechanisms for learning and cul- what is innate is not a set of rigid in-
ture to be possible in the ½rst place. Evo- structions for behavior but rather pro-
lutionary psychology has documented grams that take in information from the
hundreds of universals that cut across senses and give rise to new thoughts and
the world’s cultures, and has shown that actions. Language is a paradigm case:
many psychological traits (such as our though particular languages such as Jap-
taste for fatty foods, social status, and anese and Yoruba are not innate, the ca-
risky sexual liaisons) are better adapted pacity to acquire languages is a uniquely
to the evolutionary demands of an an- human talent. And once acquired, a lan-
cestral environment than to the actual guage is not a ½xed list of sentences, but
demands of the current environment. a combinatorial algorithm allowing an
Developmental psychology has shown in½nite number of new thoughts to be
expressed.2 Pinker, The Blank Slate; Gary F. Marcus, The
Moreover, because the mind is a com-Birth of the Mind: How a Tiny Number of Genes
Creates the Complexities of Human Thought (New plex system composed of many inter-
York: Basic Books, 2004); Matt Ridley, Nature acting parts, it makes no sense to ask
Via Nurture: Genes, Experience, and What Makes whether humans are sel½sh or generous
Us Human (London: Fourth Estate, 2003);
or nasty or noble across the board. Rath-Robert Plomin, Michael J. Owen, and Peter
er, they are driven by competing motivesMcGuf½n, “The Genetic Basis of Complex Hu-
man Behaviors,” Science 264 (1994): 1733–1739. elicited in different circumstances. And
2 Dædalus Fall 2004Pinker.qxd 09/29/04 2:54 PM Page 3
if genes affect behavior, it is not by tug- there is a widespread desire that the Why nature
& nurtureging on the muscles directly, but by their whole issue would somehow just go
won’t gointricate effects on the circuitry of a away. A common position on nature and away
growing brain. nurture among contemporary scientists
Finally, questions of what people in- can be summarized as follows:
nately have in common must be distin-
No one today believes that the mind is a
guished from questions of how races,
blank slate; to refute such a belief is to tip
sexes, or individuals innately differ. Evo-
over a straw man. All behavior is the prod-
lutionary biology gives reasons to be-
uct of an inextricable interaction between
lieve that there are systematic species-
heredity and environment during develop-
wide universals, circumscribed ways in
ment, so the answer to all nature-nurture
which the sexes differ, random quantita-
questions is “some of each.” If people only
tive variation among individuals, and
recognized this truism, the political re-
few if any differences among races and
criminations could be avoided. Moreover,3ethnic groups.
modern biology has made the very dis-
This reframing of human nature also
tinction between nature and nurture ob-
offers a rational way to address the polit-
solete. Since a given set of genes can have4ical and moral fears of human nature.
different effects in different environ-
Political equality, for example, does not
ments, there may always be an environ-
hinge on a dogma that people are innate-
ment in which a supposed effect of the
ly indistinguishable, but on a commit-
genes can be reversed or canceled; there-
ment to treat them as individuals in
fore the genes impose no signi½cant con-
spheres such as education and the crim-
straints on behavior. Indeed, genes are
inal justice system. Social progress does
expressed in response to environmental
not require that the mind be free of ig-
signals, so it is meaningless to try to dis-
noble motives, only that it have other
tinguish genes and environments; doing
motives (such as the emotion of empa-
so only gets in the way of productive re-
thy and cognitive faculties that can
search.
learn from history) that can counteract
them. The attitude is often marked by words
like ‘interactionist,’ ‘developmentalist,’
‘dialectic,’ ‘constructivist,’ and ‘epige-By now most scientists reject both the
netic,’ and is typically accompanied nineteenth-century doctrine that biolo-
by a diagram with the labels ‘genes,’gy is destiny and the twentieth-century
‘behavior,’ ‘prenatal environment,’ ‘bio-