# Actuarial Finance (ActSci)

Actuarial Finance
Organizer and Chair: Jean-Francois Renaud (Université du Québec à Montréal)
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RUNHUAN FENG, University of Illinois at Urbana-Champaign
Spectral Methods for the Valuation of Variable Annuity Guaranteed Benefits  [PDF]

Spectral methods have been extensively exploited for the pricing of exotic options, yet unknown to the risk management literature. In the first part, we demonstrate some novel applications of spectral methods for the computation of risk measures for variable annuity guaranteed minimum maturity benefit and guaranteed minimum death benefit, which is the key to determining risk-based capital according to regulatory requirements. Our examples show that spectral methods are highly efficient and numerically more stable than conventional known methods. In the second part, we explore an application of spectral methods in conjunction with probabilistic methods in the pricing of more complicated guaranteed minimum withdrawal benefit. Numerical examples are provided to demonstrate the great efficiency and accuracy of the resulting algorithm.

ANNE MACKAY, University of Waterloo
Reducing Surrender Incentives through Fee Structure in Variable Annuities  [PDF]

In this presentation, we discuss the effect the fee structure of a variable annuity on the embedded surrender option. We consider fees set as a fixed percentage of the variable annuity account, as well as regular fees set as a fixed, deterministic amount. Surrender charges are also taken into account. For fairly general premium and fee schedules, we discuss theoretical conditions under which it is never optimal for the policyholder to surrender. Using finite difference methods and partial differential equations, we present numerical examples that highlight the effect of a combination of surrender charges and deterministic fees in reducing the value of the surrender option and raising the optimal surrender boundary.

TOM SALISBURY, York University
Optimal Tontines  [PDF]

Tontines were once more popular than annuities, but have fallen out of favour. As risk charges for systemic longevity risk rise, tontines (and other alternatives to traditional annuity designs) are being reconsidered, that leave the purchaser insured against idiosyncratic but not systemic longevity. We will look at optimizing tontine design and use.