2,430 research outputs found
Zero bias transformation and asymptotic expansions II : the Poisson case
We apply a discrete version of the methodology in \cite{gauss} to obtain a
recursive asymptotic expansion for \esp[h(W)] in terms of Poisson
expectations, where is a sum of independent integer-valued random variables
and is a polynomially growing function. We also discuss the remainder
estimations
Multiple defaults and contagion risks
We study multiple defaults where the global market information is modelled as
progressive enlargement of filtrations. We shall provide a general pricing
formula by establishing a relationship between the enlarged filtration and the
reference default-free filtration in the random measure framework. On each
default scenario, the formula can be interpreted as a Radon-Nikodym derivative
of random measures. The contagion risks are studied in the multi-defaults
setting where we consider the optimal investment problem in a contagion risk
model and show that the optimization can be effectuated in a recursive manner
with respect to the default-free filtration
Multiple defaults and contagion risks
We study multiple defaults where the global market information is modelled as progressive enlargement of filtrations. We shall provide a general pricing formula by establishing a relationship between the enlarged filtration and the reference default-free filtration in the random measure framework. On each default scenario, the formula can be interpreted as a Radon-Nikodym derivative of random measures. The contagion risks are studied in the multi-defaults setting where we consider the optimal investment problem in a contagion risk model and show that the optimization can be effectuated in a recursive manner with respect to the default-free filtration.
Optimal investment with counterparty risk: a default-density modeling approach
We consider a financial market with a stock exposed to a counterparty risk
inducing a drop in the price, and which can still be traded after this default
time. We use a default-density modeling approach, and address in this
incomplete market context the expected utility maximization from terminal
wealth. We show how this problem can be suitably decomposed in two optimization
problems in complete market framework: an after-default utility maximization
and a global before-default optimization problem involving the former one.
These two optimization problems are solved explicitly, respectively by duality
and dynamic programming approaches, and provide a fine understanding of the
optimal strategy. We give some numerical results illustrating the impact of
counterparty risk and the loss given default on optimal trading strategies, in
particular with respect to the Merton portfolio selection problem
Information Asymmetry in Pricing of Credit Derivatives
We study the pricing of credit derivatives with asymmetric information. The
managers have complete information on the value process of the firm and on the
default threshold, while the investors on the market have only partial
observations, especially about the default threshold. Different information
structures are distinguished using the framework of enlargement of filtrations.
We specify risk neutral probabilities and we evaluate default sensitive
contingent claims in these cases
Optimal investment under multiple defaults risk: A BSDE-decomposition approach
We study an optimal investment problem under contagion risk in a financial
model subject to multiple jumps and defaults. The global market information is
formulated as a progressive enlargement of a default-free Brownian filtration,
and the dependence of default times is modeled by a conditional density
hypothesis. In this Ito-jump process model, we give a decomposition of the
corresponding stochastic control problem into stochastic control problems in
the default-free filtration, which are determined in a backward induction. The
dynamic programming method leads to a backward recursive system of quadratic
backward stochastic differential equations (BSDEs) in Brownian filtration, and
our main result proves, under fairly general conditions, the existence and
uniqueness of a solution to this system, which characterizes explicitly the
value function and optimal strategies to the optimal investment problem. We
illustrate our solutions approach with some numerical tests emphasizing the
impact of default intensities, loss or gain at defaults and correlation between
assets. Beyond the financial problem, our decomposition approach provides a new
perspective for solving quadratic BSDEs with a finite number of jumps.Comment: Published in at http://dx.doi.org/10.1214/11-AAP829 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling
We introduce a class of interest rate models, called the -CIR model,
which gives a natural extension of the standard CIR model by adopting the
-stable L{\'e}vy process and preserving the branching property. This
model allows to describe in a unified and parsimonious way several recent
observations on the sovereign bond market such as the persistency of low
interest rate together with the presence of large jumps at local extent. We
emphasize on a general integral representation of the model by using random
fields, with which we establish the link to the CBI processes and the affine
models. Finally we analyze the jump behaviors and in particular the large
jumps, and we provide numerical illustrations
Zero bias transformation and asymptotic expansions
International audienc
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