Valuation and Hedging of the Ruin-Contingent Life Annuity (RCLA)

Authors

  • H. Huang,

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    • H. Huang is Professor of Mathematics and Statistics at York University. M. A. Milevsky is Associate Professor of Finance, York UniversityH. Huang is Professor of Mathematics and Statistics at York University. M. A. Milevsky is Associate Professor of Finance, York University, and Executive Director of the IFID Centre. T. S. Salisbury is Professor of Mathematics and Statistics at York University, all in Toronto, Canada. The second author can be contacted via e-mail: milevsky@yorku.ca. The authors acknowledge the helpful comments from a JRI referee, as well as from seminar participants at the Department of Risk Management and Insurance at The Wharton School, seminar participants at Monash University, Melbourne, The University of New South Wales, and the University of Technology, Sydney. In particular the authors would like to acknowledge helpful comments from Carl Chiarella, Neil Doherty, Olivia Mitchell, and Eckhard Platen. Huang's and Salisbury's research is supported in part by NSERC and MITACS.
  • M. A. Milevsky,

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    • H. Huang is Professor of Mathematics and Statistics at York University. M. A. Milevsky is Associate Professor of Finance, York UniversityH. Huang is Professor of Mathematics and Statistics at York University. M. A. Milevsky is Associate Professor of Finance, York University, and Executive Director of the IFID Centre. T. S. Salisbury is Professor of Mathematics and Statistics at York University, all in Toronto, Canada. The second author can be contacted via e-mail: milevsky@yorku.ca. The authors acknowledge the helpful comments from a JRI referee, as well as from seminar participants at the Department of Risk Management and Insurance at The Wharton School, seminar participants at Monash University, Melbourne, The University of New South Wales, and the University of Technology, Sydney. In particular the authors would like to acknowledge helpful comments from Carl Chiarella, Neil Doherty, Olivia Mitchell, and Eckhard Platen. Huang's and Salisbury's research is supported in part by NSERC and MITACS.
  • T. S. Salisbury

    Search for more papers by this author
    • H. Huang is Professor of Mathematics and Statistics at York University. M. A. Milevsky is Associate Professor of Finance, York UniversityH. Huang is Professor of Mathematics and Statistics at York University. M. A. Milevsky is Associate Professor of Finance, York University, and Executive Director of the IFID Centre. T. S. Salisbury is Professor of Mathematics and Statistics at York University, all in Toronto, Canada. The second author can be contacted via e-mail: milevsky@yorku.ca. The authors acknowledge the helpful comments from a JRI referee, as well as from seminar participants at the Department of Risk Management and Insurance at The Wharton School, seminar participants at Monash University, Melbourne, The University of New South Wales, and the University of Technology, Sydney. In particular the authors would like to acknowledge helpful comments from Carl Chiarella, Neil Doherty, Olivia Mitchell, and Eckhard Platen. Huang's and Salisbury's research is supported in part by NSERC and MITACS.

Abstract

We analyze an insurance instrument called a ruin-contingent life annuity (RCLA), which is a stand-alone version of the option embedded inside a variable annuity (VA) but without the buyer having to transfer investments to the insurance company. The annuitant's payoff from an RCLA is a dollar of income per year for life, deferred until a certain wealth process hits zero. We derive the partial differential equation (PDE) satisfied by the RCLA value assuming no arbitrage, describe efficient numerical techniques, and provide estimates for RCLA values. The practical motivation is twofold. First, numerous insurance companies are now offering similar contingent deferred annuities (CDAs). Second, the U.S. Treasury and Department of Labor have encouraged DC plans to offer longevity insurance to participants and the RCLA might be the ideal product.

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