# The analytic approach for the stochastic projection of the public pension fund

Hyungsu Kim, Geonwoo Kim, Sung chul Lee

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

In this paper, we propose a stochastic method to project the public pension fund in the public pension system (PPS). For this we introduce the stochastic differential equations for the three parts: the premium revenue, the benefit expenditure, and the fund process. From these we show that the solution of the aggregated fund process is the sum of log-normals, which is approximated as one log-normal for the analytic result. Related to the parameter estimations, we implement the moment matching in the first moment. For the second moment, we apply the extreme value method following Parkinson. In order to follow Parkinson, we take the maximum and the minimum range of the fund amount based on the various sensitivity result as well as the baseline one from the deterministic projection result. In this reason, it is naturally to maintain the close interrelation with the deterministic projection result, which is very important since it is still key result in the actuarial valuation of the PPS.

Original language English 196-206 11 Probability in the Engineering and Informational Sciences 31 2 https://doi.org/10.1017/S0269964816000504 Published - 2017 Apr 1

### Fingerprint

Parameter estimation
Differential equations
Projection
Moment Matching
Moment
Stochastic Methods
Extreme Values
Valuation
Stochastic Equations
Parameter Estimation
Baseline
Pension funds
Public pensions
Differential equation
Pension system
Range of data
Stochastic differential equations
Revenue
Extreme values

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty
• Management Science and Operations Research
• Industrial and Manufacturing Engineering

### Cite this

title = "The analytic approach for the stochastic projection of the public pension fund",
abstract = "In this paper, we propose a stochastic method to project the public pension fund in the public pension system (PPS). For this we introduce the stochastic differential equations for the three parts: the premium revenue, the benefit expenditure, and the fund process. From these we show that the solution of the aggregated fund process is the sum of log-normals, which is approximated as one log-normal for the analytic result. Related to the parameter estimations, we implement the moment matching in the first moment. For the second moment, we apply the extreme value method following Parkinson. In order to follow Parkinson, we take the maximum and the minimum range of the fund amount based on the various sensitivity result as well as the baseline one from the deterministic projection result. In this reason, it is naturally to maintain the close interrelation with the deterministic projection result, which is very important since it is still key result in the actuarial valuation of the PPS.",
author = "Hyungsu Kim and Geonwoo Kim and Lee, {Sung chul}",
year = "2017",
month = "4",
day = "1",
doi = "10.1017/S0269964816000504",
language = "English",
volume = "31",
pages = "196--206",
journal = "Probability in the Engineering and Informational Sciences",
issn = "0269-9648",
publisher = "Cambridge University Press",
number = "2",

}

The analytic approach for the stochastic projection of the public pension fund. / Kim, Hyungsu; Kim, Geonwoo; Lee, Sung chul.

In: Probability in the Engineering and Informational Sciences, Vol. 31, No. 2, 01.04.2017, p. 196-206.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The analytic approach for the stochastic projection of the public pension fund

AU - Kim, Hyungsu

AU - Kim, Geonwoo

AU - Lee, Sung chul

PY - 2017/4/1

Y1 - 2017/4/1

N2 - In this paper, we propose a stochastic method to project the public pension fund in the public pension system (PPS). For this we introduce the stochastic differential equations for the three parts: the premium revenue, the benefit expenditure, and the fund process. From these we show that the solution of the aggregated fund process is the sum of log-normals, which is approximated as one log-normal for the analytic result. Related to the parameter estimations, we implement the moment matching in the first moment. For the second moment, we apply the extreme value method following Parkinson. In order to follow Parkinson, we take the maximum and the minimum range of the fund amount based on the various sensitivity result as well as the baseline one from the deterministic projection result. In this reason, it is naturally to maintain the close interrelation with the deterministic projection result, which is very important since it is still key result in the actuarial valuation of the PPS.

AB - In this paper, we propose a stochastic method to project the public pension fund in the public pension system (PPS). For this we introduce the stochastic differential equations for the three parts: the premium revenue, the benefit expenditure, and the fund process. From these we show that the solution of the aggregated fund process is the sum of log-normals, which is approximated as one log-normal for the analytic result. Related to the parameter estimations, we implement the moment matching in the first moment. For the second moment, we apply the extreme value method following Parkinson. In order to follow Parkinson, we take the maximum and the minimum range of the fund amount based on the various sensitivity result as well as the baseline one from the deterministic projection result. In this reason, it is naturally to maintain the close interrelation with the deterministic projection result, which is very important since it is still key result in the actuarial valuation of the PPS.

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U2 - 10.1017/S0269964816000504

DO - 10.1017/S0269964816000504

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JO - Probability in the Engineering and Informational Sciences

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