Zelda Marino

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.

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.

Algorithm 944: Talbot Suite: Parallel Implementations of Talbot's Method for the Numerical Inversion of Laplace Transforms

We present Talbot Suite, a C parallel software collection for the numerical inversion of Laplace Transforms, based on Talbots method. It is designed to fit both single and multiple Laplace inversion problems, which arise in several application and research fields. In our software, we achieve high accuracy and efficiency, making full use of modern architectures and introducing two different levels of parallelism: coarse and fine grained parallelism. They offer a reasonable tradeoff between accuracy, the main aspect for a few inversions, and efficiency, the main aspect for multiple inversions. To take into account modern high-performance computing architectures, Talbot Suite provides different software versions: an OpenMP-based version for shared memory machines and a MPI-based version for distributed memory machines. Moreover, oriented to hybrid architectures, a combined MPI/OpenMP-based implementation is provided too. We describe our parallel algorithms and the software organization. We also report some performance results. Our software includes sample programs to call the Talbot Suite functions from C and from MATLAB.

Wavelet techniques for option pricing on advanced architectures

This work focuses on the development of a parallel pricing algorithm for Asian options based on the Discrete Wavelet Transform. Following the approach proposed in [6], the pricing process requires the solution of a set of independent Fredholm integral equations of the second kind. Within this evaluation framework, our aim is to develop a robust parallel pricing algorithm based on wavelet techniques for the pricing problem of discrete monitoring arithmetic Asian options. In particular, the Discrete Wavelet Transform is applied in order to approximate the kernels of the integral equations. We discuss both the accuracy of the method and its scalability properties.

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 general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Levy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.

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.

Tuning a Deep Learning Network for Solvency II: Preliminary Results

Under the Solvency II Directive, insurance and reinsurance undertakings are required to perform continuous monitoring of risks and market consistent valuation of assets and liabilities. Solvency II application is particularly demanding, both theoretically and under the computational point of view. At present, any technique able to improve on accuracy or to reduce computing time is highly desirable. This works reports initial results on the design of a Deep Learning Network, aimed to reduce computing time by avoiding the standard full nested Monte Carlo approach.

Stock price forecasting with an hybrid model

Prediction of market prices is an important and well-researched problem. While traditional techniques have yielded good results, rooms for improvement still exists, especially in the ability to explain sudden changes in behavior, as a response to shocks. Nonlinear systems have been successfully used to describe phase transitions in deterministic chaotic systems, so the combination of the expressive power of nonlinear systems and the efficient computation of linear models is an attractive idea. On such basis, in this work, an hybrid model is proposed that tunes its regression parameters with the results of nonlinear tools. Experiments, performed on several stocks in diverse sector and markets, show interesting performances, confirming as well the presence of distinct phases in the stock evolution, characterized by distinctly separated dynamics. Mathematics Subject Classification: 34A34, 62J02

Financial Evaluation of Life Insurance Policies in High Performance ComputingEnvironments

The European Directive Solvency II has increased the request of stochastic asset–liability management models for insurance undertakings. The Directive has established that insurance undertakings can develop their own “internal models” for the evaluation of values and risks in the contracts. In this chapter, we give an overview on some computational issues related to internal models. The analysis is carried out on “Italian style” profit-sharing life insurance policies (PS policy) with minimum guaranteed return. We describe some approaches for the development of accurate and efficient algorithms for their simulation. In particular, we discuss the development of parallel software procedures. Main computational kernels arising in models employed in this framework are stochastic differential equations (SDEs) and high-dimensional integrals. We show how one can develop accurate and efficient procedures for PS policies simulation applying different numerical methods for SDEs and techniques for accelerating Monte Carlo simulations for the evaluation of the integrals. Moreover, we show that the choice of an appropriate probability measure provides a significative gain in terms of accuracy.