Integral representations of some functionals of fractional Brownian motion

We prove change of variables formulas [It\^o formulas] for functions of both arithmetic and geometric averages of geometric fractional Brownian motion. They are valid for all convex functions, not only for smooth ones. These change of variables formulas provide us integral representations of functions of average in the sense of generalized Lebesgue-Stieltjes integral

ELSI: The Finnish pension microsimulation model

This report is an overview of the structure and functionalities of the pension microsimulation model ELSI. Developed and maintained by the Finnish Centre for Pensions, ELSI is used to simulate the life courses of individuals in order to forecast the long-term development of Finnish earnings-related pensions and national and guarantee pensions

Eläkkeelle siirtymisen kannustimien arviointi mikrosimulointilaskelmilla

Raportissa esitetään laskelmia, kuinka paljon loppuelinkaaren tulot muuttuvat eri tulokäsitteillä, jos eläkkeelle siirtymistä lykkää alimman vanhuuseläkeiän yli. Tarkastelussa ovat vuosina 1954–1984 syntyneet ikäluokat. Laskelmat on laadittu ELSI-mikrosimulointimallilla

Partition of the Life Course: An Extended Dynamic Microsimulation Analysis

This study explores life courses in a dynamic microsimulation framework at a time of high public interest in prolonging working lives. We provide new insights into how historical records could be merged with microsimulation outcomes and develop a new indicator for measuring and illustrating individual life course stages in adulthood. Partition of the life course yields the average lengths of life course stages in Finland. We illustrate our indicator and its distribution by gender, cohort and level of education. The proposed indicator is also used to elaborate widely accepted indicators from the Pension Adequacy Report. We conclude that the proposed partitioning method should be easily transferrable to other countries where historical records are available

Syntyvyysskenaarioiden vaikutukset työeläkkeiden rahoitukseen

Raportissa esitetään eläkelaskelmia, jotka perustuvat väestötieteellisesti perusteltuihin skenaarioihin syntyvyyden tulevasta kehityksestä

Using sequence analysis to visualize and validate model transitions

Peer reviewe