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Optimal Multistage Defined-Benefit Pension Fund Management

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Handbook of Recent Advances in Commodity and Financial Modeling

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 257))

Abstract

We present an asset-liability management (ALM) model designed to support optimal strategic planning by a defined benefit (DB) occupational pension fund (PF) manager. PF ALM problems are by nature long-term decision problems with stochastic elements affecting both assets and liabilities. Increasingly PFs operating in the second pillar of modern pension systems are subject to mark-to-market accounting standards and constrained to monitor their risk capital exposure over time. The ALM problem is formulated as a multi-stage stochastic program (MSP) with an underlying scenario tree structure in which decision stages are combined with non-decision annual stages aimed at mapping carefully the evolution of PF’s liabilities. We present a case-study of an underfunded PF with an initial liquidity shortage and show how a dynamic policy, relying on a set of specific decision criteria, is able to gain a long-term equilibrium solvency condition over a 20 year horizon.

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Acknowledgements

This research includes the formulation of a pension fund ALM problem reflecting a real-world case-study developed in cooperation between Allianz Investment Management and University of Bergamo. The presented numerical evidence has been modified and rescaled for confidentiality reasons but it does reflect actual operational conditions and the presented results remain valid.

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Authors and Affiliations

  1. Department of Management, Economics and Quantitative Methods, University of Bergamo, Bergamo, Italy

    Giorgio Consigli, Vittorio Moriggia, Elena Benincasa, Giacomo Landoni, Filomena Petronio & Sebastiano Vitali

  2. Allianz Investment Management, Allianz Group, Munich, Germany

    Massimo di Tria, Mario Skoric & Angelo Uristani

Authors
  1. Giorgio Consigli
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  2. Vittorio Moriggia
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  3. Elena Benincasa
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  4. Giacomo Landoni
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  5. Filomena Petronio
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  6. Sebastiano Vitali
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  7. Massimo di Tria
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  8. Mario Skoric
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  9. Angelo Uristani
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Corresponding author

Correspondence to Giorgio Consigli .

Editor information

Editors and Affiliations

  1. Department of Management, Economics and Quantitative Methods, University of Bergamo, Bergamo, Italy

    Giorgio Consigli

  2. Department of Statistics and Quantitative Methods, University of Milan Bicocca, Milano, Italy

    Silvana Stefani

  3. Department of Statistics and Quantitative Methods, University of Milan Bicocca, Milano, Italy

    Giovanni Zambruno

Appendix

Appendix

In Tables 13.2 and 13.3 we show the estimated statistical parameters adopted to generate correlated quarterly returns through a Monte Carlo simulation (Glasserman, 2003; Consigli et al., 2012a) for each benchmark i and node n. Once the return scenarios are aggregated in tree form, they are passed to an algebraic language deterministic model generator, to produce the stochastic program deterministic equivalent instance (Consigli and Dempster, 1998). The returns’ statistics have been estimated on an historical window composed of 63 observations starting from the first quarter of 1999 till the third quarter of 2014.

Table 13.2 Average annual price (ρ) and income (ξ) returns of the entire asset universe. These parameters are estimated as the historical mean value of time series from January 1, 1999 to December 31, 2014. Data are in percentage
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Table 13.3 Estimated variance-covariance matrix of the price annual returns with historical data from January 1, 1999 to December 31, 2014 of the asset universe: EURIBOR 3m (E-3m), Treasury (T), Securitized (Sec), Corporate Investment Grade (IG) and High Yield (HY), Real Estate (R-E), Equity (Eq) and TIPS
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Consigli, G. et al. (2018). Optimal Multistage Defined-Benefit Pension Fund Management. In: Consigli, G., Stefani, S., Zambruno, G. (eds) Handbook of Recent Advances in Commodity and Financial Modeling. International Series in Operations Research & Management Science, vol 257. Springer, Cham. https://doi.org/10.1007/978-3-319-61320-8_13

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