977 research outputs found
Dynamics of multivariate default system in random environment
We consider a multivariate default system where random environmental
information is available. We study the dynamics of the system in a general
setting and adopt the point of view of change of probability measures. We also
make a link with the density approach in the credit risk modelling. In the
particular case where no environmental information is concerned, we pay a
special attention to the phenomenon of system weakened by failures as in the
classical reliability system
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
A lending scheme for a system of interconnected banks with probabilistic constraints of failure
We derive a closed form solution for an optimal control problem related to an
interbank lending schemes subject to terminal probability constraints on the
failure of banks which are interconnected through a financial network. The
derived solution applies to a real banks network by obtaining a general
solution when the aforementioned probability constraints are assumed for all
the banks. We also present a direct method to compute the systemic relevance
parameter for each bank within the network
Central Clearing Valuation Adjustment
This paper develops an XVA (costs) analysis of centrally cleared trading,
parallel to the one that has been developed in the last years for bilateral
transactions. We introduce a dynamic framework that incorporates the sequence
of cash-flows involved in the waterfall of resources of a clearing house. The
total cost of the clearance framework for a clearing member, called CCVA for
central clearing valuation adjustment, is decomposed into a CVA corresponding
to the cost of its losses on the default fund in case of defaults of other
member, an MVA corresponding to the cost of funding its margins and a KVA
corresponding to the cost of the regulatory capital and also of the capital at
risk that the member implicitly provides to the CCP through its default fund
contribution. In the end the structure of the XVA equations for bilateral and
cleared portfolios is similar, but the input data to these equations are not
the same, reflecting different financial network structures. The resulting XVA
numbers differ, but, interestingly enough, they become comparable after scaling
by a suitable netting ratio
Information-Based Models for Finance and Insurance
In financial markets, the information that traders have about an asset is reflected in its
price. The arrival of new information then leads to price changes. The ‘information-based
framework’ of Brody, Hughston and Macrina (BHM) isolates the emergence of
information, and examines its role as a driver of price dynamics. This approach has
led to the development of new models that capture a broad range of price behaviour.
This thesis extends the work of BHM by introducing a wider class of processes for the
generation of the market filtration. In the BHM framework, each asset is associated
with a collection of random cash flows. The asset price is the sum of the discounted
expectations of the cash flows. Expectations are taken with respect (i) an appropriate
measure, and (ii) the filtration generated by a set of so-called information processes that
carry noisy or imperfect market information about the cash flows. To model the flow
of information, we introduce a class of processes termed Levy random bridges (LRBs),
generalising the Brownian and gamma information processes of BHM. Conditioned on
its terminal value, an LRB is identical in law to a Levy bridge. We consider in detail
the case where the asset generates a single cash flow XT at a fixed date T. The flow
of information about XT is modelled by an LRB with random terminal value XT.
An explicit expression for the price process is found by working out the discounted
conditional expectation of XT with respect to the natural filtration of the LRB. New
models are constructed using information processes related to the Poisson process, the
Cauchy process, the stable-1/2 subordinator, the variance-gamma process, and the
normal inverse-Gaussian process. These are applied to the valuation of credit-risky
bonds, vanilla and exotic options, and non-life insurance liabilities
Markov decision process algorithms for wealth allocation problems with defaultable bonds
This paper is concerned with analysing optimal wealth allocation techniques within a defaultable financial market similar to Bielecki and Jang (2007). It studies a portfolio optimization problem combining a continuous-time jump market and a defaultable security; and presents numerical solutions through the conversion into a Markov decision process and characterization of its value function as a unique fixed point to a contracting operator. This work analyses allocation strategies under several families of utilities functions, and highlights significant portfolio selection differences with previously reported results
A maximum principle for a stochastic control problem with multiple random terminal times
In the present paper we derive, via a backward induction technique, and ad
hoc maximum principle for an optimal control problem with multiple random
terminal times. Therefore we apply the aforementioned result to the case of a
linear quadratic controller, providing solutions for the optimal control in
terms of Riccati backward SDE with random terminal time. Eventually all the
above results are applied to a system of interconnected banks
A maximum principle for a stochastic control problem with multiple random terminal times
In the present paper we derive, via a backward induction technique, an ad hoc maximum principle for an optimal control problem with multiple random terminal times. We thus apply the aforementioned result to the case of a linear quadratic controller, providing solutions for the optimal control in terms of Riccati backward SDE with random terminal time
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