6,731 research outputs found
What happens after a default: the conditional density approach
We present a general model for default time, making precise the role of the
intensity process, and showing that this process allows for a knowledge of the
conditional distribution of the default only "before the default". This lack of
information is crucial while working in a multi-default setting. In a single
default case, the knowledge of the intensity process does not allow to compute
the price of defaultable claims, except in the case where immersion property is
satisfied. We propose in this paper the density approach for default time. The
density process will give a full characterization of the links between the
default time and the reference filtration, in particular "after the default
time". We also investigate the description of martingales in the full
filtration in terms of martingales in the reference filtration, and the impact
of Girsanov transformation on the density and intensity processes, and also on
the immersion property
Coherent Price Systems and Uncertainty-Neutral Valuation
We consider fundamental questions of arbitrage pricing arising when the
uncertainty model is given by a set of possible mutually singular probability
measures. With a single probability model, essential equivalence between the
absence of arbitrage and the existence of an equivalent martingale measure is a
folk theorem, see Harrison and Kreps (1979). We establish a microeconomic
foundation of sublinear price systems and present an extension result. In this
context we introduce a prior dependent notion of marketed spaces and viable
price systems. We associate this extension with a canonically altered concept
of equivalent symmetric martingale measure sets, in a dynamic trading framework
under absence of prior depending arbitrage. We prove the existence of such sets
when volatility uncertainty is modeled by a stochastic differential equation,
driven by Peng's G-Brownian motions
Asymptotics of Asynchronicity
In this article we focus on estimating the quadratic covariation of
continuous semimartingales from discrete observations that take place at
asynchronous observation times. The Hayashi-Yoshida estimator serves as
synchronized realized covolatility for that we give our own distinct
illustration based on an iterative synchronization algorithm. We consider
high-frequency asymptotics and prove a feasible stable central limit theorem.
The characteristics of non-synchronous observation schemes affecting the
asymptotic variance are captured by a notion of asymptotic covariations of
times. These are precisely illuminated and explicitly deduced for the important
case of independent time-homogeneous Poisson sampling.Comment: technical report, 36 page
The filtering equations revisited
The problem of nonlinear filtering has engendered a surprising number of
mathematical techniques for its treatment. A notable example is the
change-of--probability-measure method originally introduced by Kallianpur and
Striebel to derive the filtering equations and the Bayes-like formula that
bears their names. More recent work, however, has generally preferred other
methods. In this paper, we reconsider the change-of-measure approach to the
derivation of the filtering equations and show that many of the technical
conditions present in previous work can be relaxed. The filtering equations are
established for general Markov signal processes that can be described by a
martingale-problem formulation. Two specific applications are treated
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