THESIS
2013
Abstract
In this thesis, we study three different problems in financial risk management.
The first one is to prove that the sample autocovariance with lag 1 (ACV(1))
of the increments of a mixed Poisson process converges to 0 almost surely as
the sample size goes to infinity. Pólya processes, as a good candidate for modeling
the arrival of events that cluster in time, are also mixed Poisson processes.
The sample ACV(1) of the increments of a Pólya process converges to 0, instead
of the theoretical population ACV(1) of the increments, almost surely as
the sample size goes to infinity, implying that one cannot use sample ACV in
parameter estimation of Pólya process by methods of moments. The second
problem is about comparing the power of backtest of value-at-risk at level 1 %
and ex...[
Read more ]
In this thesis, we study three different problems in financial risk management.
The first one is to prove that the sample autocovariance with lag 1 (ACV(1))
of the increments of a mixed Poisson process converges to 0 almost surely as
the sample size goes to infinity. Pólya processes, as a good candidate for modeling
the arrival of events that cluster in time, are also mixed Poisson processes.
The sample ACV(1) of the increments of a Pólya process converges to 0, instead
of the theoretical population ACV(1) of the increments, almost surely as
the sample size goes to infinity, implying that one cannot use sample ACV in
parameter estimation of Pólya process by methods of moments. The second
problem is about comparing the power of backtest of value-at-risk at level 1 %
and expected shortfall at level 2%. With simulation, we show that 2% expected
shortfall performs better than 1 % value-at-risk in detecting the misspecification
of the forecast model. The third problem is about representation of risk measures
incorporating uncertainty in probability measures. We propose a new set
of axioms for risk measures and obtain representation of the risk measures that
satisfy these axioms. The representation of the new class of risk measures, called
natural risk measures, provide a theoretical framework that includes the Basel
II and the Basel III risk measures as special cases.
Post a Comment