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Credit risk transfer and financial sector performance
In this paper we study the impact of credit risk transfer (CRT) on the stability and the efficiency of a financial system in a model with endogenous intermediation and production. Our analysis suggests that with respect to CRT, the individual incentives of the agents in the economy are generally aligned with social incentives. Hence, CRT does not pose a systematic challenge to the functioning of the financial system and is generally welfare enhancing. However, we identify issues that should be addressed by the regulatory authorities in order to minimize the potential costs of CRT. These include: ensuring the development of new methods of CRT that allow risk to be more perfectly transferred, setting regulatory standards that reflect differences in the social cost of instability in the banking and insurance sector; promoting CRT instruments that are nor detrimental to the monitoring incentives of banks
Congruences for powers of the partition function
Let denote the number of partitions of into colors. In
analogy with Ramanujan's work on the partition function, Lin recently proved in
\cite{Lin} that for every integer . Such
congruences, those of the form , were
previously studied by Kiming and Olsson. If is prime and , then such congruences satisfy . Inspired by Lin's example, we obtain natural infinite families of such
congruences. If (resp. and
) is prime and (resp.
and ), then for , where , we have that
\begin{equation*} p_{-t}\left(\ell
n+\frac{r(\ell^2-1)}{24}-\ell\Big\lfloor\frac{r(\ell^2-1)}{24\ell}\Big\rfloor\right)\equiv0\pmod{\ell}.
\end{equation*} Moreover, we exhibit infinite families where such congruences
cannot hold
Multiquadratic fields generated by characters of
For a finite group , let denote the field generated over
by its character values. For , G. R. Robinson and J. G.
Thompson proved that where
. Confirming a speculation of Thompson, we show
that arbitrary suitable multiquadratic fields are similarly generated by the
values of -characters restricted to elements whose orders are only
divisible by ramified primes. To be more precise, we say that a -number is
a positive integer whose prime factors belong to a set of odd primes . Let be the field generated by the
values of -characters for even permutations whose orders are
-numbers. If , then we determine a constant with the
property that for all , we have
K_{\pi}(A_n)=\mathbb{Q}\left(\sqrt{p_1^*}, \sqrt{p_2^*},\dots,
\sqrt{p_t^*}\right).$
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