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DTSTART:20070311T020000
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DTSTAMP:20260727T104702
DTSTART;TZID=America/Detroit:20260923T160000
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SUMMARY:Workshop / Seminar:Buying Time: Optimal Service Purchase and Retirement Timing in Defined Benefit Plans
DESCRIPTION:We study retirement timing decisions in a defined benefit (DB) pension plan with a service-purchase\noption. An employee who would otherwise retire at a fixed time T may elect to purchase L additional\nyears of service and retire early. Earlier retirement provides additional leisure but requires an upfront\npayment and typically results in a reduced post-retirement income stream. We model this trade-off in\na continuous-time retirement framework by allowing the employee to choose L to maximize the value\nof wealth and leisure at retirement in both deterministic and life-contingent settings. Our model\ncaptures a common feature of public pension systems: early retirement is often accompanied by both\nan upfront cost and a permanent reduction in benefits. We show that this structure yields tractable\nand intuitive results in several benchmark cases\, including settings without mortality risk and settings\nwith mortality risk under simplifying assumptions. In more general cases\, we characterize optimal\nbehavior through comparative statics and numerical examples. A key insight is that the interaction\nbetween the finite-horizon value of leisure and the lifetime cost embedded in pension pricing can\ngenerate a range of behaviors\, including monotone strategies and interior optima. While many results\nalign with economic intuition\, others require more careful interpretation. We also extend the model to\nallow for dynamic decision-making via a multi-period service-purchase option\, solved by backward\ninduction. The results provide insight into optimal retirement timing and the role of plan design in\nshaping participant behavior. This is joint work with David Kausch and Virginia Young.
UID:149578-21906720@events.umich.edu
URL:https://events.umich.edu/event/149578
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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