University & Research

Download a zipped file which includes the PDF slides used in lecture #1, where I introduced the types of problems we will solve in the course, instructions on how to download and install R-studio together with some basic R-scripts.

Download a zipped file which includes a (hypothetical) personal finance dataset in csv format, a number of R-scripts and the PDF slides used for lecture #2, in which we code-up a basic model of spending and saving over the lifecycle and compare with the data.

Download a zipped file which includes a number of R-scripts and the PDF slides used for lecture #3, in which we discuss how to model and measure the longevity of a portfolio subject to withdrawals, basic Monte Carlo (MC) simulations and the sequence of returns (SoR) effect.

Download a zipped file which includes a number of plot R-scripts, data files and the PDF slides used for lecture #4, in which we introduce and discuss basic cohort mortality tables, the implied mortality rates and the concept of a random remaining lifetime, all in discrete time. And, some financial economics at the very end.

Download a zipped file which includes a number of R-scripts, data files and the PDF slides used for lecture #5, in which we discuss period vs. cohort mortality tables, the Gompertz-Makeham law of mortality, estimating parameters via regression, projection factors and reduction scales, the Compensation Law of Mortality (CLaM), simulating random lifetimes and a brief discussion of biological versus chronological age.

Download a zipped file which includes a number of R-scripts, data files and the PDF slides used for lecture #6, in which discuss the lump-sum versus pension annuity dilemma, the valuation of life annuities under the Gompertz law of mortality, the general valuation of longevity-contingent claims via the Binomial distribution, the Law of Large Numbers and finally, we locate some mortality credits.

Download a zipped folder which includes the PDF slides used for lecture #7, in which I discuss modeling Defined Benefit (DB) versus Defined Contribution (DC) pensions, coding-up Monte Carlo simulation of DC account values at retirement in R, discussion of typical DB benefit formulas and whether or not to delay your pension (e.g. CPP or OAS) in exchange for higher benefits in the future, all under idealized conditions.

Download a zipped folder which includes PDF slides and R-scripts used for lecture #8, in which I discuss and solve the (Fisher-Yaari) retirement lifecycle model (LCM) with Gompertz mortality, the optimal consumption spending rate, and the wealth depletion time (WDT) in the presence of pension income.

Download a zipped folder which contains all the homework assignment questions with the final project used in the Winter 2019 semester plus an advanced reading list. The folder also contains a complete collection of all the R-scripts with a few extra ones I have used in some recent technical papers, all in one centralized location. (Note there are only 8 weeks of formal lecture notes. The other sessions were used to solve problems and for guest lectures.)

This presentation focuses on how to think about and model Covid-19 in continuous-time, from the perspective of life-cycle financial economics and retirement income planning. To begin with, it hypothesizes that total mortality rates during the coronavirus period have been strictly proportional to normal mortality rates, which effectively increase biological ages across the curve, otherwise known as a parallel shift of the (Gompertzian) term structure. The presentation then goes on to provide some preliminary empirical evidence from the UK and Europe corroborating the parallel shift hypothesis, and discusses the implications of a (arguably, convenient) parallel shift on the utility-based valuation of life annuities. The main practical message here is that longevity insurance becomes more – as opposed to less – valuable, even if life expectancies decline. The presentation concludes by proposing the so-called compensation law of mortality (CLM) as a possible alternative to a parallel shift, and briefly discusses how to merge a CLM into a stochastic lifecycle model of investment and consumption. These slides are from the One World Actuarial Research Seminar (OWARS) Lecture, delivered on 20 May 2020, in the very early stages of Covid-19 and was intended to provide an overview of research. (Note that this version contains low-resolution images to reduce the size of the PDF, but a high-resolution version is available from Amazon.)

Most insurance actuaries work with discrete (qx) mortality tables while academic researchers in actuarial finance (such as myself) prefer to operate with continuous mortality rates such as the Gompertz Law for example. In this stand-alone technical note I explain how to properly go from tables to curves and how to minimize the distance between the two (coming soon.)