Course 2 Life and Pensions


This course addresses issues that arise in the context of retirement provision and life insurance. Long-dated liabilities and intergenerational solidarity are key terms.


Having completed this course you should be able to value life insurance and pension liabilities and perform ALM analyses including longevity risk. You should also be able to participate in debates concerning pension systems and longevity, at policy level as well as at the level of underlying models.


Detailed contents are as follows.


  1. Asset Management; optimal portfolio choice.

    We will first review the asset side of the pension fund balance sheet, covering such concepts as asset classification, mean-variance analysis, Sharpe ratios, the Capital Asset Pricing Model, and beta. We will then look beyond mean-variance analysis, taking into account higher moments of the return distribution, like skewness and kurtosis. You will make a case study on optimal portfolio choice.


  1. Term structure modelling; Valuation of long-maturity liabilities; inflation risk; Long-run investments; nominal versus real term structures


We will introduce models for the term structure of interest rates that will be used to value liabilities, and we will analyze how ALM models, using inflation, (real) interest rates and stock returns as the relevant state variables, can be used to conveniently summarize the behavior of assets and liabilities on the pension fund balance sheet. You will make a case study in class. At this stage, longevity risk is ignored.


  1. Modelling of mortality dynamics; Longevity risk: measurement and management; Effect of longevity risk on pension liabilities; Asset Liability Management; risk mitigating strategies.

    We will start by discussing state-of-the-art literature regarding mortality dynamics, starting from the seminal work by Lee and Carter, and then proceeding to more recent developments. Next, we will discuss the impact of longevity risk on pension and insurance providers, and we will extend ALM models to include longevity risk. We then analyze different methods to mitigate longevity and mortality risk. We will consider contracts that involve external financial parties, such as longevity swaps and survivor bonds, but also constructions that implement internal risk sharing mechanisms between different subgroups within a pension provider.  We discuss the difficulties in establishing a market price for longevity risk, quantify the effectiveness of possible risk mitigation solutions for different types of stakeholders, and we also take a look at implementation issues such as longevity basis spreads and counterparty risk.


  1. Supervision models; nFTK and Solvency; supervision on keeping promises in case of stated ambitions; Transparency regarding future purchasing power of pension entitlements.

    We will first focus on pension regulation in the Netherlands, covering the following topics: funding ratio, solvency buffers, ultimate forward rate, recovery plans, indexation cuts, pension results. We will then also spend time on the historical evolution of Dutch pension regulation, and make international comparisons. You will combine the above-described models to make a case study on the calculation of a pension fund’s required solvency.


Learning outcomes

Upon completion of the course, participants will be able to participate in debates concerning pension systems and longevity, at the policy level as well as at the level of the underlying models.




Lecture notes / presentation to be distributed by lecturer.


Campbell & Viceira (2005), “The Term Structure of the Risk-Return Trade-Off,” Financial Analysts Journal, Vol. 61, No. 1, p. 34—44


Pitacco, E., Denuit, M., & Haberman, S. (2009). Modelling longevity dynamics for pensions and annuity business. Oxford University Press.


De Waegenaere, A., Melenberg, B., & Stevens, R. (2010). Longevity risk. De Economist, 158(2), 151-192. Supervision on pension funds




Please make sure the software is installed before Meeting 1.


  • Tilburg Finance Tool: please install this free download via

  • Excel: please activate the Solver: Open Excel – click on the Office button on the left top – you will see a few options; at the bottom you will see “Excel Options” – you will then enter a menu with a few options on the left - please choose Add-ins – at the bottom you see Manage Excel Add-ins – click on GO – there you will find the option Solver Add-in at the bottom – choose this option and then click OK.



R. (Rob) van den Goorbergh Ph.D.

prof. dr. B. (Bertrand) Melenberg

dr. N.F.F. (Nikolaus) Schweizer

prof. dr. ir. M.H. (Michel) Vellekoop



Written exam.