arXiv subjects

Vilislav Boutchaktchiev

Publications and source records attributed to Vilislav Boutchaktchiev.

3 recordsLinked to original sources

arXiv2018

A Markov Chain Model for the Cure Rate of Non-Performing Loans

A Markov-chain model is developed for the purpose estimation of the cure rate of non-performing loans. The technique is performed collectively, on portfolios and it can be applicable in the process of calculation of credit impairment. It is efficient in terms of data manipulation costs which makes it accessible even to smaller financial institutions. In addition, several other applications to portfolio optimization are suggested.

q-fin.RM↗

arXiv2013

Local Mixed Hodge Structure on Brill-Noether Stacks

On a smooth algebraic curve X with genus greater than 1 we consider a flat principal bundle with a reductive structure group S and a vector bundle associated with it. To this set of information we put in correspondence a pro-algebraic group on whose functional algebra we introduce a mixed Hodge structure. This construction, in fact, works for any smooth algebraic variety X which, considered as an analytic space, has a nonabelian first homotopy group, and the rest are trivial. The Hodge structure defined in this way can be expressed in terms of iterated integrals. Furthermore, considered in the context of previous work by C. Simpson, this MHS is the local mixed Hodge structure on a nonabelian cohomological space on X with coefficients into a Brill-Noether stack, i.e., a stack with two non-trivial homotopy groups: a fundamental group isomorphic to the group S and an n-th homotopy group represented by a vector space, the fiber of the vector bundle discussed above above. My construction is compatible and generalizes the work of R. Hain on Hodge structure on relative Malcev completion of the fundamental group of X.

math.AG↗

arXiv2013

Nonabelian Mixed Hodge Structure on Brill-Noether Stacks

A Brill-Noether stack is an algebraic very presentable stack whose homotopy type has two nontrivial homotopy groups. We consider one with a fundamental group --- a reductive algebraic group-scheme S and one higher homotopy group, represented by a vector space V. The homotopy type also defines an action of S on V. This stack is used as coefficient space for nonabelian cohomological space on a smooth algebraic variety X. We define nonabelian MHS on cohomological spaces of this type in the context of the work of C. Simpson related to MHS on the space of local systems. It is defined via an action of the multiplicative complex group on a appropriately chosen category. The exhibited structure in fact generalizes Simpson's work. Allowing a more general type of coefficient stack. Furthermore, the so-defined MHS, when considered at a vicinity of an object, which remains fixed under the structural action of C*, produces the local MHS on Brill-Noether Stacks as defined in our earlier work. The nonabelian mixed Hodge structure on a Brill-Noether stack is a example of the mixed Hodge structure on a schematic homotopy type, studied by Katzarkov, Pantev and Toen. It has the advantage, due to the relative simplicity of the coefficient stack, that it could be locally written out in terms of iterated integrals.

math.AG↗