# Simulating a Worst Case Social Security Model

Topics: Time, Simulation, Model Pages: 5 (1131 words) Published: May 3, 2013
Kenji L Logie

Modeling Simulation Final Project

Simulating a Worst Case Social Security Model System of Interest For the purpose of this simulation a simplified worst case social security model was created for a developing country’s social security program. The program simulates how long it would take this new social security program to go bankrupt, if it earns no interest on its capital, and its only source of paying out benefits is members’ monthly contributions and its initial capital of \$750,000. This model only deals with paying into the social security for the purpose of retirement benefits. Persons pay into the social security program at one of three possible earning levels monthly. This would lead to one of three possible payouts of benefits monthly for persons 60 years or older. Simulating the point of bankruptcy begins at the third part of the program when the organization has built up capital over a period of time, which is defined within the simulation as the contribution only period without paying out any benefits. At the end of the contribution only period it begins to pay out benefits to anyone in the simulation eligible to receive benefits which by definition is a members who is 60 years or older. Events and System Variables Events: a new person joins the work force, payment of benefits, and receiving contributions

Page 1 of 20

Kenji L Logie

Modeling Simulation Final Project

System State variables: c- Social Security capital, n- Maximum number of persons in the system at that point in time t- Time Discrete Event Simulation The simulation represents a discrete event simulation. The events all take place chronologically, and represent state changes at a particular point in the simulation. The simulation begins with the creation of a fixed number of persons, and the time at which a new person joining the workforce is generated from an exponential distribution to move time forward. This step is followed by generating more times persons joining the workforce, payment of benefits or receiving contribution; an increment of one since time in the simulation is measured in months. Each event moves time forward until the capital of the social security becomes negative; the point of termination in the simulation. Worst Case Social Security Model The simulation represents a Poisson Process. Each inter arrival time of a person to the workforce is independent of the person before them and it occurs at a rate specified within the simulation.

Page 2 of 20

Kenji L Logie

Modeling Simulation Final Project

The simulation is a terminating simulation. The simulation ends when the social security office becomes bankrupt. This event occurs when the amount of cash paid out exceeds the amount currently held by the social security office.

The following simplification assumptions were made for the purpose of the model or imposed by restrictions of the program used to simulate the model:  The maximum number of persons the system can accommodate is 90000 persons.  There are only three levels of contributions and benefit payments.  The simulation time variables are all measured in months.  The simulations values of capital, benefits and payments all in \$100,000.  Persons join the workforce at a random age between 18 and 60 and only leave the workforce at retirement.  Persons live to a life expectancy based on their gender; 70 years for males and 76 years for females.  The population ratio for males to females is approximately 1:1. The input distribution was exponential and was chosen based on data provided by the Social Security the simulation was modeled on. Purpose of performing simulation

Page 3 of 20

Kenji L Logie

Modeling Simulation Final Project

The purpose of the simulation is to calculate how long it takes for a simulation to go bankrupt. From this initial question the rate of joining the workforce, return on capital and the contribution period were all varied individually...