174 research outputs found
Continuation Value Methods for Sequential Decisions: A General Theory
After the introductory chapter, this thesis comprises four main
chapters before concluding in chapter 6. The thesis undertakes a
systematic analysis of the con- tinuation value based method for
sequential decision problems originally due to Jovanovic (1982).
Although recently this technique is widely employed in a va-
riety of economic applications, its theoretical connections to
the traditional value function based method, relative efficiency,
and optimality/analytical properties have hitherto received no
general investigation. The thesis fills this gap.
On the one hand, the thesis shows that the operator employed by
this method (referred to below as the Jovanovic operator) is
semiconjugate to the traditional Bellman operator and has
essentially equivalent dynamic properties. In particu- lar, under
general assumptions, any fixed point of one of the operators is a
direct translation of a fixed point of the other. Iterative
sequences generated by the operators are also simple
translations. After adding topological structure to the generic
setting, the thesis shows that the Bellman and Jovanovic
operators are both contraction mappings under identical
assumptions, and that convergence to the respective fixed points
occurs at the same rate.
To ensure sufficient generality for economic applications, the
optimality and sym- metry analysis has been embedded separately
in (a) spaces of potentially un- bounded functions endowed with
generic weighted supremum norm distances, and (b) spaces of
integrable functions with divergence measured by Lp norms.
Unbounded rewards are allowed provided that they do not cause
continuation values to diverge. Moreover, the theory mentioned
above is established for im- portant classes of sequential
decision problems, including:
• standard optimal stopping problems (chapter 2),
• repeated optimal stopping problems (chapter 3), and
• dynamic discrete choice problems (chapter 4).
On the other hand, despite these similarities, the thesis shows
that there do re- main important differences between the
continuation value based method and the traditional value
function based method in terms of efficiency and analytical
convenience.
One of these differences concerns the dimensionality of the
effective state spaces associated with the Bellman and Jovanovic
operators. First, aside from a class of problems for which the
continuation dynamics are trivial, the effective state space of
the continuation value function is never larger than that of the
value function. Second, for a broad class of sequential problems,
the effective state space of the continuation value function is
strictly lower dimensional than that of the value function.
Another key difference is that continuation value functions are
typi- cally smoother than value functions. The relative
smoothness comes from taking expectations over stochastic
transitions. In each scenario, it is highly advanta- geous to
work with the continuation value method rather than the
traditional value function method.
The thesis systematically characterizes these hidden advantages
in terms of model primitives and provides a range of important
applications (chapters 2 and 5). Moreover, by exploiting these
advantages, the thesis develops a general theory for sequential
decision problems based around continuation values and obtains a
range of new results on optimality, optimal behavior and
efficient computation (chapter 5)
A Review on Textless Back Translation of China-Themed Works Written in English
Textless back translation here refers to the kind of back translation in which the translator retranslates China-themed works written in English language back into Chinese language. In recent years, the phenomenon of textless back translation has begun to draw a closer attention from the academic circles and arouse heated discussions among scholars and experts. This paper, starting from back translation, aims to review the previous studies on textless back translation of China-themed works written in English in terms of definition, classification as well as related studies both at home and abroad. Furthermore, authors of the paper attempt to propose several deficiencies that need to be tackled in future studies: (a) inconsistent use of terms; (b) the lack of comparative studies between textless back translation and back translation in general; (c) the lack of systematic theoretical studies on textless back translation and the studies that treat textless back translation as a separate category of translation studies.
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