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

Homogeneización de problemas (elasto)hidrodinámicos en lubricación

El presente trabajo trata sobre la homogeneización de un problema de lubricación, utilizando técnicas de doble escala. Se plantea un problema acoplado de tipo Reynolds Hertzcon cavitación Elrod-Adams, que contempla la presencia de efectos debidos a superficies rugosas con oscilaciones periódicas. La geometría de la rugosidad depende de un pequeño parámetro asociado a la frecuencia de la misma. Entre las dificultades para la homogeneización del problema elastohidrodinámico destacamos el caracter no lineal asociado a la frontera libre del modelo de cavitación, los aspectos no locales del modelo de Hertz y la ley de viscosidad no lineal. Además de establecer los resultados de convergencia al problema homogeneizado , para un problema con datos reales se presentan resultados obtenidos con métodos numéricos adecuados, comparando el modelo dependiente del pequeño parámetro y el modelo homogeneizado.Ministerio de Educación y Cienci

Resolución numérica de un problema de frontera libre asociado a inversiones con efectos medioambientales irreversibles

En este trabajo se proponen métodos numéricos para resolver el problema planteado en [3] J. I. Díaz, C. Faghloumi, Analysis of a degenerate obstacle problem on an unbounded set arising in the environment, Appl. Math. Optim., 45 (2002), 251–267 para modelar la utilidad conjunta resultante de abordar, en el instante óptimo, un proceso industrial que tiene ciertos beneficios y conlleva efectos irreversibles sobre el medio ambiente. El modelo se plantea como un problema de tipo obstáculo asociado a una ecuación elíptica en un dominio no acotado. Siguiendo una idea de [3] J. I. Díaz, C. Faghloumi, Analysis of a degenerate obstacle problem on an unbounded set arising in the environment, Appl. Math. Optim.,45 (2002), 251–267, se propone un cambio de variable que lo reduce a un dominio acotado. A continuación se proponen algoritmos de tipo Gauss–Seidel con proyección y Lions–Mercier para resolver el problema discretizado por elementos finitos; este último se combina con técnicas multimalla y de refinamiento adaptativo. La eficiencia de los algoritmos se ilustra mediante ejemplos con solución analítica conocida

Invited talks of the CEDYA/CMA 2022, Zaragoza, Spain

The biennial congress CEDYA/CMA 2022 of the Spanish Society of Applied Mathematics, SEMA, was held in Zaragoza in July 2022 in a hybrid format. In this Special Issue of the SEMA Journal, we gather the papers of five of the invited plenary speakers of the conference

Matemáticas del planeta Tierra : unidad didáctica

Con: Matemáticas del planeta Tierra : [cuaderno de actividades] / Fernando Alcaide, Miguel NietoResumen basado en el de la publicaciónRevisor didáctico: Luis RicoEsta unidad didáctica nace dentro de una iniciativa internacional de gran relevancia, la proclamación de 2013 como Año de las Matemáticas del Planeta Tierra (Mathematics Planet Earth, MPE 2013). Esta declaración ha tenido su origen en las sociedades matemáticas e institutos de investigación de Estados Unidos y Canadá, y posteriormente ha recibido el apoyo de la Unión Matemática Internacional (IMU) y la UNESCO. El objetivo del MPE 2013 es señalar la importancia de las matemáticas para conocer y gestionar mejor el funcionamiento de nuestro planeta –su propia estructura, la vida que alberga, los fenómenos en su corteza, en su atmósfera y en sus océanos, la influencia de la actividad humana, nuestro entorno astronómico– y también para estar mejor preparados ante catástrofes que nos alcanzan a veces de una manera terrible. Se ha dividido la obra en 16 capítulos, desarrollado cada uno de ellos por expertos en el tema y con materiales complementarios (libros, películas, series televisivas, portales de Internet) que pueden resultar de utilidad en las clases para amenizar e ilustrar los textos.ES

PROREPAIR-B: A Prospective Cohort Study of the Impact of Germline DNA Repair Mutations on the Outcomes of Patients With Metastatic Castration-Resistant Prostate Cancer

[Purpose] Germline mutations in DNA damage repair (DDR) genes are identified in a significant proportion of patients with metastatic prostate cancer, but the clinical implications of these genes remain unclear. This prospective multicenter cohort study evaluated the prevalence and effect of germline DDR (gDDR) mutations on metastatic castration-resistance prostate cancer (mCRPC) outcomes.[Patients and Methods] Unselected patients were enrolled at diagnosis of mCRPC and were screened for gDDR mutations in 107 genes. The primary aim was to assess the impact of ATM/BRCA1/BRCA2/PALB2 germline mutations on cause-specific survival (CSS) from diagnosis of mCRPC. Secondary aims included the association of gDDR subgroups with response outcomes for mCRPC treatments. Combined progression-free survival from the first systemic therapy (PFS) until progression on the second systemic therapy (PFS2) was also explored.[Results] We identified 68 carriers (16.2%) of 419 eligible patients, including 14 with BRCA2, eight with ATM, four with BRCA1, and none with PALB2 mutations. The study did not reach its primary end point, because the difference in CSS between ATM/BRCA1/BRCA2/PALB2 carriers and noncarriers was not statistically significant (23.3 v 33.2 months; P = .264). CSS was halved in germline BRCA2 (gBRCA2) carriers (17.4 v 33.2 months; P = .027), and gBRCA2 mutations were identified as an independent prognostic factor for CCS (hazard ratio [HR], 2.11; P = .033). Significant interactions between gBRCA2 status and treatment type (androgen signaling inhibitor v taxane therapy) were observed (CSS adjusted P = .014; PFS2 adjusted P = .005). CSS (24.0 v 17.0 months) and PFS2 (18.9 v 8.6 months) were greater in gBRCA2 carriers treated in first line with abiraterone or enzalutamide compared with taxanes. Clinical outcomes did not differ by treatment type in noncarriers.[Conclusion] gBRCA2 mutations have a deleterious impact on mCRPC outcomes that may be affected by the first line of treatment used. Determination of gBRCA2 status may be of assistance for the selection of the initial treatment in mCRPC. Nonetheless, confirmatory studies are required before these results can support a change in clinical practice.Supported by an unrestricted grant from Fundación Cris contra el cancer; three investigator awards from the Prostate Cancer Foundation (C.C.P. [2013], D.O. [2014], and E.C. [2017]); and three grants from Fondo de Investigación Sanitaria, Instituto de Salud Carlos III (No. PI13/01287 and PI16/01565 to D.O. and No. PI15/01471 to P.L.). During the conduct of this study, E.C., D.O., P.N., and L.M.-P. were supported by grants from Ministerio de Economía, Industria y Competitividad (No. JCI-2014-19129 [E.C.], No. RYC-2015-18625 [D.O.], No. SVP-2013-067937 [P.N.], No. SVP-2014-068895 [L.M.]); D.O. was also funded by a Return fellowship from Fundación Científica de la Asociación Española Contra el Cancer, 2012-2015; N.R.L. and R.L., by grants from Instituto de Salud Carlos III (No. CM14-00200 to N.R.L. and No. CM17-00221 [R.L.]); and Y.C., by a grant from Ministerio de Educación, Cultura y Deportes (No. FPU15/05126). C.C.P. was supported by a congressional-designated medical research program award (No. CMRP-PC131820).Peer reviewe