72,914 research outputs found
Rate-optimal Bayesian intensity smoothing for inhomogeneous Poisson processes
We apply nonparametric Bayesian methods to study the problem of estimating
the intensity function of an inhomogeneous Poisson process. We exhibit a prior
on intensities which both leads to a computationally feasible method and enjoys
desirable theoretical optimality properties. The prior we use is based on
B-spline expansions with free knots, adapted from well-established methods used
in regression, for instance. We illustrate its practical use in the Poisson
process setting by analyzing count data coming from a call centre.
Theoretically we derive a new general theorem on contraction rates for
posteriors in the setting of intensity function estimation. Practical choices
that have to be made in the construction of our concrete prior, such as
choosing the priors on the number and the locations of the spline knots, are
based on these theoretical findings. The results assert that when properly
constructed, our approach yields a rate-optimal procedure that automatically
adapts to the regularity of the unknown intensity function
Analytic solutions for Hamilton-Jacobi-Bellman equations
Closed form solutions are found for a particular class of Hamilton- Jacobi-Bellman equations emerging from a differential game among fims competing over quantities in a simultaneous oligopoly framework. After the derivation of the solutions, a microeconomic example in a non-standard market is presented where feedback equilibrium is calculated with the help of one of the previous formulas
Intersection types for unbind and rebind
We define a type system with intersection types for an extension of
lambda-calculus with unbind and rebind operators. In this calculus, a term with
free variables, representing open code, can be packed into an "unbound" term,
and passed around as a value. In order to execute inside code, an unbound term
should be explicitly rebound at the point where it is used. Unbinding and
rebinding are hierarchical, that is, the term can contain arbitrarily nested
unbound terms, whose inside code can only be executed after a sequence of
rebinds has been applied. Correspondingly, types are decorated with levels, and
a term has type decorated with k if it needs k rebinds in order to reduce to a
value. With intersection types we model the fact that a term can be used
differently in contexts providing different numbers of unbinds. In particular,
top-level terms, that is, terms not requiring unbinds to reduce to values,
should have a value type, that is, an intersection type where at least one
element has level 0. With the proposed intersection type system we get
soundness under the call-by-value strategy, an issue which was not resolved by
previous type systems.Comment: In Proceedings ITRS 2010, arXiv:1101.410
Option Pricing in an Imperfect World
In a model with no given probability measure, we consider asset pricing in
the presence of frictions and other imperfections and characterize the property
of coherent pricing, a notion related to (but much weaker than) the no
arbitrage property. We show that prices are coherent if and only if the set of
pricing measures is non empty, i.e. if pricing by expectation is possible. We
then obtain a decomposition of coherent prices highlighting the role of
bubbles. eventually we show that under very weak conditions the coherent
pricing of options allows for a very clear representation from which it is
possible, as in the original work of Breeden and Litzenberger, to extract the
implied probability. Eventually we test this conclusion empirically via a new
non parametric approach.Comment: The paper has been withdrawn because in the newer version it was
split into two different papers, each of which have been uploaded into Arxi
Feedforward data-aided phase noise estimation from a DCT basis expansion
This contribution deals with phase noise estimation from pilot symbols. The phase noise process is approximated by an expansion of discrete cosine transform (DCT) basis functions containing only a few terms. We propose a feedforward algorithm that estimates the DCT coefficients without requiring detailed knowledge about the phase noise statistics. We demonstrate that the resulting (linearized) mean-square phase estimation error consists of two contributions: a contribution from the additive noise, that equals the Cramer-Rao lower bound, and a noise independent contribution, that results front the phase noise modeling error. We investigate the effect of the symbol sequence length, the pilot symbol positions, the number of pilot symbols, and the number of estimated DCT coefficients it the estimation accuracy and on the corresponding bit error rate (PER). We propose a pilot symbol configuration allowing to estimate any number of DCT coefficients not exceeding the number of pilot Symbols, providing a considerable Performance improvement as compared to other pilot symbol configurations. For large block sizes, the DCT-based estimation algorithm substantially outperforms algorithms that estimate only the time-average or the linear trend of the carrier phase. Copyright (C) 2009 J. Bhatti and M. Moeneclaey
A note on market completeness with American put options
We consider a non necessarily complete financial market with one bond and one risky asset, whose price process is modelled by a suitably integrable, strictly positive, càdlàg process over . Every option price is defined as the conditional expectation under a given equivalent (true) martingale measure , the same for all options. We show that every positive contingent claim on can be approximately replicated (in -sense) by investing dynamically in the underlying and statically in all American put options (of every strike price and with the same maturity ). We also provide a counter-example to static hedging with European call options of all strike prices and all maturities .
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