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Will Jumps Ruin Your Retirement? A Moment Matching Perspective

31 Pages Posted: 7 May 2011  

Mirela Cara

York University - Department of Mathematics & Statistics

Huang Huaxiong

York University

Moshe A. Milevsky

York University - Schulich School of Business

Date Written: December 5, 2010

Abstract

We derive an expression for the lifetime ruin probability (LRP), defined as the probability a fixed consumption plan will deplete an investment portfolio prior to a retiree's stochastic time of death, assuming the investment return driving the portfolio obeys a jump-diffusion process. This is in contrast to previous literature that assumes geometric Brownian motion (GBM) dynamics. Our model leads to a partial-integro differential equation (PIDE) for the LRP and some related probabilities. We then compare our PIDE values to GBM-based probabilities using moment matching techniques calibrated to historical equity returns. Our main result is that despite naive initial intuition that “jumps make things worse,” in the context of retirement risk management this is not necessarily the case. Our ruin probabilities are lower ceteris paribus. In the body of the paper, we explain why this is the case. Our results should be of interest to scholars and practitioners who are concerned with sustainable income strategies for retirees, in a defined contribution (DC) world.

Keywords: Personal Finance, Portfolio Choice, Investment Decisions, Optimization Techniques

JEL Classification: G11, D14, C61, G22, D91

Suggested Citation

Cara, Mirela and Huaxiong, Huang and Milevsky, Moshe A., Will Jumps Ruin Your Retirement? A Moment Matching Perspective (December 5, 2010). Available at SSRN: https://ssrn.com/abstract=1832616 or http://dx.doi.org/10.2139/ssrn.1832616

Mirela Cara

York University - Department of Mathematics & Statistics ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Huang Huaxiong

York University ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Moshe Arye Milevsky (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

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