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Richard B. Sowers

  1. Large Portfolio Asymptotics for Loss From Default.

    Wed, 09/07/2011 - 15:01 — SomNambul
    Authors: Konstantinos Spiliopoulos, Richard B. Sowers, Kay Giesecke, Justin A. Sirignano
    Subjects: Risk Management
    Abstract

    We prove a law of large numbers for the loss from default and use it for
    approximating the distribution of the loss from default in large, potentially
    heterogenous portfolios. The density of the limiting measure is shown to solve
    a non-linear SPDE, and the moments of the limiting measure are shown to satisfy
    an infinite system of SDEs. The solution to this system leads to %the solution
    to the SPDE through an inverse moment problem, and to the distribution of the
    limiting portfolio loss, which we propose as an approximation to the loss
    distribution for a large portfolio.

  2. Default Clustering in Large Portfolios: Typical and Atypical Events.

    Tue, 04/12/2011 - 15:01 — SomNambul
    Authors: Konstantinos Spiliopoulos, Richard B. Sowers, Kay Giesecke
    Subjects: Risk Management
    Abstract

    We develop a dynamic point process model of correlated default timing in a
    portfolio of firms, and analyze typical and atypical default profiles in the
    limit as the size of the pool grows. In our model, a name defaults at a
    stochastic intensity that is influenced by an idiosyncratic risk process, a
    systematic risk process common to all names, and past defaults. We prove a law
    of large numbers for the default rate in the pool, which describes the
    "typical" behavior of defaults.

  3. Recovery Rates in investment-grade pools of credit assets: A large deviations analysis.

    Tue, 06/15/2010 - 15:01 — SomNambul
    Authors: Konstantinos Spiliopoulos, Richard B. Sowers
    Subjects: Risk Management
    Abstract

    We consider the effect of recovery rates on a pool of credit assets. We allow
    the recovery rate to depend on the defaults in a general way. Using the theory
    of large deviations, we study the structure of losses in a pool consisting of a
    continuum of types. We derive the corresponding rate function and show that it
    has a natural interpretation as the favored way to rearrange recoveries and
    losses among the different types. Numerical examples are also provided.

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