9,173 research outputs found
Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach
We propose an efficient method to evaluate callable and putable bonds under a
wide class of interest rate models, including the popular short rate diffusion
models, as well as their time changed versions with jumps. The method is based
on the eigenfunction expansion of the pricing operator. Given the set of call
and put dates, the callable and putable bond pricing function is the value
function of a stochastic game with stopping times. Under some technical
conditions, it is shown to have an eigenfunction expansion in eigenfunctions of
the pricing operator with the expansion coefficients determined through a
backward recursion. For popular short rate diffusion models, such as CIR,
Vasicek, 3/2, the method is orders of magnitude faster than the alternative
approaches in the literature. In contrast to the alternative approaches in the
literature that have so far been limited to diffusions, the method is equally
applicable to short rate jump-diffusion and pure jump models constructed from
diffusion models by Bochner's subordination with a L\'{e}vy subordinator
Instruction sequences for the production of processes
Single-pass instruction sequences under execution are considered to produce
behaviours to be controlled by some execution environment. Threads as
considered in thread algebra model such behaviours: upon each action performed
by a thread, a reply from its execution environment determines how the thread
proceeds. Threads in turn can be looked upon as producing processes as
considered in process algebra. We show that, by apposite choice of basic
instructions, all processes that can only be in a finite number of states can
be produced by single-pass instruction sequences.Comment: 23 pages; acknowledgement corrected, reference update
On tiered small jump operators
Predicative analysis of recursion schema is a method to characterize
complexity classes like the class FPTIME of polynomial time computable
functions. This analysis comes from the works of Bellantoni and Cook, and
Leivant by data tiering. Here, we refine predicative analysis by using a
ramified Ackermann's construction of a non-primitive recursive function. We
obtain a hierarchy of functions which characterizes exactly functions, which
are computed in O(n^k) time over register machine model of computation. For
this, we introduce a strict ramification principle. Then, we show how to
diagonalize in order to obtain an exponential function and to jump outside
deterministic polynomial time. Lastly, we suggest a dependent typed
lambda-calculus to represent this construction
On the expressiveness of single-pass instruction sequences
We perceive programs as single-pass instruction sequences. A single-pass
instruction sequence under execution is considered to produce a behaviour to be
controlled by some execution environment. Threads as considered in basic thread
algebra model such behaviours. We show that all regular threads, i.e. threads
that can only be in a finite number of states, can be produced by single-pass
instruction sequences without jump instructions if use can be made of Boolean
registers. We also show that, in the case where goto instructions are used
instead of jump instructions, a bound to the number of labels restricts the
expressiveness.Comment: 14 pages; error corrected, acknowledgement added; another error
corrected, another acknowledgement adde
Connected Operators for the Totally Asymmetric Exclusion Process
We fully elucidate the structure of the hierarchy of the connected operators
that commute with the Markov matrix of the Totally Asymmetric Exclusion Process
(TASEP). We prove for the connected operators a combinatorial formula that was
conjectured in a previous work. Our derivation is purely algebraic and relies
on the algebra generated by the local jump operators involved in the TASEP.
Keywords: Non-Equilibrium Statistical Mechanics, ASEP, Exact Results,
Algebraic Bethe Ansatz.Comment: 10 page
R-matrix approach to integrable systems on time scales
A general unifying framework for integrable soliton-like systems on time
scales is introduced. The -matrix formalism is applied to the algebra of
-differential operators in terms of which one can construct infinite
hierarchy of commuting vector fields. The theory is illustrated by two
infinite-field integrable hierarchies on time scales which are difference
counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer
soliton systems are constructed as related finite-field restrictions.Comment: 21 page
The Veblen functions for computability theorists
We study the computability-theoretic complexity and proof-theoretic strength
of the following statements: (1) "If X is a well-ordering, then so is
epsilon_X", and (2) "If X is a well-ordering, then so is phi(alpha,X)", where
alpha is a fixed computable ordinal and phi the two-placed Veblen function. For
the former statement, we show that omega iterations of the Turing jump are
necessary in the proof and that the statement is equivalent to ACA_0^+ over
RCA_0. To prove the latter statement we need to use omega^alpha iterations of
the Turing jump, and we show that the statement is equivalent to
Pi^0_{omega^alpha}-CA_0. Our proofs are purely computability-theoretic. We also
give a new proof of a result of Friedman: the statement "if X is a
well-ordering, then so is phi(X,0)" is equivalent to ATR_0 over RCA_0.Comment: 26 pages, 3 figures, to appear in Journal of Symbolic Logi
A thread calculus with molecular dynamics
We present a theory of threads, interleaving of threads, and interaction
between threads and services with features of molecular dynamics, a model of
computation that bears on computations in which dynamic data structures are
involved. Threads can interact with services of which the states consist of
structured data objects and computations take place by means of actions which
may change the structure of the data objects. The features introduced include
restriction of the scope of names used in threads to refer to data objects.
Because that feature makes it troublesome to provide a model based on
structural operational semantics and bisimulation, we construct a projective
limit model for the theory.Comment: 47 pages; examples and results added, phrasing improved, references
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A bounded jump for the bounded Turing degrees
We define the bounded jump of A by A^b = {x | Exists i <= x [phi_i (x)
converges and Phi_x^[A|phi_i(x)](x) converges} and let A^[nb] denote the n-th
bounded jump. We demonstrate several properties of the bounded jump, including
that it is strictly increasing and order preserving on the bounded Turing (bT)
degrees (also known as the weak truth-table degrees). We show that the bounded
jump is related to the Ershov hierarchy. Indeed, for n > 1 we have X <=_[bT]
0^[nb] iff X is omega^n-c.e. iff X <=_1 0^[nb], extending the classical result
that X <=_[bT] 0' iff X is omega-c.e. Finally, we prove that the analogue of
Shoenfield inversion holds for the bounded jump on the bounded Turing degrees.
That is, for every X such that 0^b <=_[bT] X <=_[bT] 0^[2b], there is a Y
<=_[bT] 0^b such that Y^b =_[bT] X.Comment: 22 pages. Minor changes for publicatio
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