Francesca Perla

On parallel asset-liability management in life insurance: a forward risk-neutral approach

In this paper we discuss the development of a valuation system of asset-liability management of portfolios of life insurance policies on advanced architectures. According to the new rules of the Solvency II project, numerical simulations must provide reliable estimates of the relevant quantities involved in the contracts; therefore, valuation processes have to rely on accurate algorithms able to provide solutions in a suitable turnaround time. Our target is to develop an effective valuation software. At this aim we first introduce a change of numeraire in the stochastic processes for risks sources, thus providing estimates under the forward risk-neutral measure that result in a gain in accuracy. We then parallelize the Monte Carlo method to speed-up the simulation process.

A PARALLEL BLOCK LANCZOS ALGORITHM FOR DISTRIBUTED MEMORY ARCHITECTURES

Abstract In this paper we propose a block Lanczos algorithm suitable for MIMD distributed memory message passing architectures. It is based on an efficient parallelizaiion of basic linear algebra operations, such as matrix-matrix, sparse matrix-matrix, and dense QR factorization. We assume an unidirectional ring as connection topology and a block column wrap-around matrices distribution. We have chosen this approach to improve load-balancing, to eliminate the intersection of messages and to decrease communication The parallel Lanczos algorithm has been tested on a Convex Meta Series, a cluster of HP Series 9000 workstations running the PVM communication system. Results of the performance evaluation based on some classical parameters are shown.

Participating life insurance policies: an accurate and efficient parallel software for COTS clusters

In this paper we discuss the development of a parallel software for the numerical simulation of Participating Life Insurance Policies in distributed environments. The main computational kernels in the mathematical models for the solution of the problem are multidimensional integrals and stochastic differential equations. The former is solved by means of Monte Carlo method combined with the Antithetic Variates variance reduction technique, while differential equations are approximated via a fully implicit, positivity-preserving, Euler method. The parallelization strategy we adopted relies on the parallelization of Monte Carlo algorithm. We implemented and tested the software on a PC Linux cluster.

Relevant applications of Monte Carlo simulation in Solvency II

The definition of solvency for insurance companies, within the European Union, is currently being revised as part of Solvency II Directive. The new definition induces revolutionary changes in the logic of control and expands the responsibilities in business management. The rationale of the fundamental measures of the Directive cannot be understood without reference to probability distribution functions. Many insurers are struggling with the realisation of a so-called “internal model” to assess risks and determine the overall solvency needs, as requested by the Directive. The quantitative assessment of the solvency position of an insurer relies on Monte Carlo simulation, in particular on nested Monte Carlo simulation that produces very hard computational and technological problems to deal with. In this paper, we address methodological and computational issues of an “internal model” designing a tractable formulation of the very complex expectations resulting from the “market-consistent” valuation of fundamental measures, such as Technical Provisions, Solvency Capital Requirement and Probability Distribution Forecast, in the solvency assessment of life insurance companies. We illustrate the software and technological solutions adopted to integrate the Disar system—an asset–liability computational system for monitoring life insurance policies—in advanced computing environments, thus meeting the demand for high computing performance that makes feasible the calculation process of the solvency measures covered by the Directive.

Traffic matrix estimation with software-defined NFV: Challenges and opportunities

Abstract Traffic matrices, abstract representations of demand, are essential for network operators endeavoring to model, measure, maintain, and improve the efficiency of their complex and heterogeneous architectures. Traffic matrix estimation consists in inferring a traffic matrix from link-level measurements. Provoked by the need to enable agile deployment of new services while, at the same time, slashing operating expenditure and energy consumption, the trend in telecommunications is to shift functionality from physical appliances to virtualized services. We analyze the effects of this landscape change on traffic matrices, their dynamics, and their estimation, indicating some new challenges and problems that will arise in all the associated modeling, analysis and evaluation activities.

Kremm: an E-learning System for Mathematical Models Applied to Economics and Finance

The widespread use of computing tools and Internet technologies that allow both distance learning and access to large amount of data and information, makes the process of solving a technical/scientific problem, much more realistic, exciting and stimulating than a few years ago, due to lack of appropriate calculation tools. However, usability of information by students and teachers at various levels, seems to be extremely limited, both due to the diversity and fragmentation of the available material, and for the large gap between the different components that should characterize science and, in particular, modern mathematics. KREMM (Knowledge Repository of Mathematical Models) is an e-learning system for the study of mathematics for economics and finance. The purpose of KREMM is to provide a significant aid in educational and pedagogical use of mathematical and statistical techniques in the context of economic and social disciplines, which starting from the creation of material on these issues, comes to propose a complete learning path.

A parallel modified block Lanczos' algorithm for distributed memory architectures

In this paper we propose a parallel block Lanczos algorithm suitable for MIMD distributed memory message passing architectures. We first consider a direct parallelization of the classic block Lanczos algorithm and we evaluate its performance. Then, after a discussion of these results, we reorganize the block algorithm obtaining a modified version that has a better behaviour with respect to the performance in the considered computing environment. We assume a unidirectional ring as connection topology and a block column wrap-around matrices distribution. We have chosen this approach to improve load-balancing, to eliminate the intersection of messages and to decrease communication. The two parallel block Lanczos algorithms have been tested on a Convex Meta Series, a cluster of HP Series 9000 workstations, running the PVM communication system.<<ETX>>

Fuzzy Contagion Cascades in Financial Networks

Previous literature shows that financial networks are sometimes described by fuzzy data. This paper extends classical models of financial contagion to the framework of fuzzy financial networks. The degree of default of a bank in the network consists in a (real valued) measure of the fuzzy default and it is computed as a fixed point for the dynamics of a modified ”fictitious default algorithm”. Finally, the algorithm is implemented in MATLAB and tested numerically on a real data set.

Numerical Solution of the Regularized Portfolio Selection Problem

We investigate the use of Bregman iteration method for the solution of the portfolio selection problem, both in the single and in the multi-period case. Our starting point is the classical Markowitz mean-variance model, properly extended to deal with the multi-period case. The constrained optimization problem at the core of the model is typically ill-conditioned, due to correlation between assets. We consider l1-regularization techniques to stabilize the solution process, since this has also relevant financial interpretations.

On the measure of contagion in fuzzy financial networks

Abstract Previous literature shows that financial networks are sometimes described by fuzzy data. This paper aims to extend classical models of financial contagion to the framework of fuzzy financial networks. The degree of default of each bank in the network is defined. It consists in a (real valued) measure of the fuzzy default and it is computed as a fixed point for the dynamics of a modified “fictitious default algorithm”. Two specific models of degree of default are also introduced and investigated; namely, an optimistic model and a pessimistic one. Finally, the algorithm is implemented in Matlab and tested numerically on a real data set.