Mathematical analysis and numerical methods for pricing pension plans allowing early retirement

In this paper, we address the mathematical analysis and numerical solution of a model for pricing a defined benefit pension plan. More precisely, the benefits received by the member of the plan depend on the average salary and early retirement is allowed. Thus, the mathematical model is posed as an obstacle problem associated to a Kolmogorov equation in the time region where the salary is being averaged. Previously to the initial averaging date, a nonhomogeneous one factor Black-Scholes equation is posed. After stating the model, existence and regularity of solutions are studied. Moreover, appropriate numerical methods based on a Lagrange-Galerkin discretization and an augmented Lagrangian active set method are proposed. Finally, some numerical examples illustrate the performance of the numerical techniques and the properties of the solution and the free boundary.retirement plans, options pricing, Kolmogorov equations, complementarity problem, numerical methods, augmented Lagrangian formulation

Economic and Social Cohesion in the EU: a critical approach

Economic and Social Cohesion is one of the principal aims of European Union according to the Treaty. Although it has a clear and rather well defined political dimension, there is not a unique definition that permits a technical definition. ¿Has an increase of Economic and Social Cohesion been observed in recent decades? ¿How could this be measured? To answer these two questions it is necessary to define, first, what is the acceptable degree of regional inequalities and, second, which could be the variables or indexes to measure it properly (not only GDP per capita). The aim of this paper is to propose new answers to the problem, using REGIO database and applying multicriteria methods. We have researched a new empirical approach to the European Cohesion and we have calculated the accomplishment of a higher Economic and Social Cohesion between the European regions. The period analysed is 1987-1999 and the results are rather shocking and suggestive, particularly compared to the ones arising from the most conventional analysis on the evolution of GDP per capita. Key words: Social and Economic Cohesion; Regional Convergence; EU Regional Policy, multicriteria methods.

Improving wireless multicast communications with NC: performance assessment over a COTS platform

Multicast services are believed to play a relevant role in next wireless networking scenarios. In this paper we exploit Tunable Sparse Network Coding techniques to increase reliability of multicast communications. We show that the proposed network coding scheme yields a better performance than state-of-the-art solutions, which are traditionally based on retransmissions. We first use a model to analytically compare the two approaches. Then, we validate and broaden this analysis by means of an experimental campaign over a testbed deployed with Commercial Of-The-Shelf devices. This platform, comprising low cost devices (Raspberry-PI), allows us to assess the feasibility of the proposed solution, which offers a relevant gain in terms of performance.This work has been supported by the Spanish Government (Ministerio de Economía y Competitividad, Fondo Europeo de Desarrollo Regional, FEDER) by means of the project ADVICE (TEC2015-71329-C2-1-R)

Mathematical analysis of obstacle problems for pricing fixed-rate mortgages with prepayment and default options

[Abstract] In this paper, we address the mathematical analysis of a partial differential equation model for pricing fixed-rate mortgages with prepayment and default options, where the underlying stochastic factors are the house price and the interest rate. The mathematical model is posed in terms of a sequence of linked complementarity problems, one for each month of the loan life, associated with a uniformly parabolic operator. We study the existence of a strong solution to each one of the obstacle problems.This work has been partially funded by Spanish MINECO (Grant numbers MTM2013-47800-C2-1-P and MTM2016-76497-R) and Xunta de Galicia grant GRC2014/044, including FEDER funds.Xunta de Galicia; GRC2014/04

Pricing pension plans based on average salary without early retirement: partial differential equation modeling and numerical solution

[Abstract] In this paper, a partial differential equation model for the pricing of pension plans based on average salary is posed by using the dynamic hedging methodology. The existence and uniqueness of solutions for the resulting initial-value problem associated with a Kolmogorov equation is obtained. Moreover, a numerical method based on a Crank–Nicolson characteristics time discretization combined with finite elements to approximate the solution is proposed. Finally, some test examples illustrate the performance of the numerical methods as a tool for pricing these pension plans.This paper was partly funded by MCINN (Project MTM2010–21135–C02-01) and by Xunta de Galicia (Project INCITE09105339PR and Ayuda CN2011/004, cofinanced with FEDER funds).Xunta de Galicia; INCITE09105339PRXunta de Galicia; CN2011/00

A new numerical method for pricing fixed-rate mortgages withprepayment and default options

[Abstract] In this paper we consider the valuation of fixed-rate mortgages including prepayment and default options,where the underlying stochastic factors are the house price and the interest rate. The mathematical modelto obtain the value of the contract is posed as a free boundary problem associated to a partial differentialequation (PDE) model. The equilibrium contract rate is determined by using an iterative process. Moreover,appropriate numerical methods based on a Lagrange–Galerkin discretization of the PDE, an augmentedLagrangian active set method and a Newton iteration scheme are proposed. Finally, some numerical resultsto illustrate the performance of the numerical schemes, as well as the qualitative and quantitative behaviourof solution and the optimal prepayment boundary are presentedPaper funded by Spanish MCINN (Project MTM2010–21135–C02-01) and by Xunta de Galicia (Ayuda CN2011/004,partially funded with FEDER funds.Xunta de Galicia; CN2011/00

Pricing pension plans under jump–diffusion models for the salary

[Abstract] In this paper we consider the valuation of a defined benefit pension plan in the presence of jumps in the underlying salary and including the possibility of early retirement. We will consider that the salary follows a jump–diffusion model, thus giving rise to a partial integro-differential equation (PIDE). After posing the model, we propose the appropriate numerical methods to solve the PIDE problem. These methods mainly consists of Lagrange–Galerkin discretizations combined with augmented Lagrangian active set techniques and with the explicit treatment of the integral term. Finally, we compare the numerical results with those ones obtained with Monte Carlo techniques.This paper has been partially funded by MCINN (Project MTM2010-21135-C02-01 and MTM2013-47800-C2-1-P) and by Xunta de Galicia (Ayuda GRC2014/044, partially funded with FEDER funds).Xunta de Galicia; GRC2014/04

Effects of jump-diffusion models for the house price dynamics in the pricing of fixed-rate mortgages, insurance and coinsurance

[Abstract] In the pricing of fixed rate mortgages with prepayment and default options, we introduce jump-diffusion models for the house price evolution. These models take into account sudden changes in the price (jumps) during bubbles and crisis situations in real estate markets. After posing the models based on partial-integro differential equations (PIDE) problems for the contract, insurance and the fraction of the total loss not covered by the insurance (coinsurance), we propose appropriate numerical methods to solve them.This work has been partially funded by MINECO of Spain (Project MTM2013-47800-C2-1-P)

De la búsqueda de la función de la proteína Vmp1 a la caracterización de la autofagia en 'Dictyostelium discoideum'

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Facultad de Medicina, Departamento de Bioquímica. Fecha de lectura: 10 de Junio de 201