(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

Features of Financial Returns Modelling Price Volatility Forecasting Standard Deviations The Accuracy of Autocorrelation Estimates Testing the Random Walk Hypothesis Forecasting Trends in Prices Evidence Against the Efficiency of Futures Markets Valuing Options Appendix: A Computer Program for Modelling Financial Time Series.

Modelling Financial Time Series

寿命研究とHuman Mortality Database

We omit Gompertz’ method of fitting, which the reader will find in Makeham, below. Also omitted are Gompertz’ mortality tables, and his discussion of life expectancy and annuities under his Law. The hyperbolic logarithms in Art. 5 are the natural logs; we are not able to follow completely his integration, which is by Newton's method of fluxions.

On the Nature of the Function Expressive of the Law of Human Mortality

In examining basis risk in index longevity hedges, it is important not to ignore the dependence between the population underlying the hedging instrument and the population being hedged. We consider four extensions to the Lee-Carter model that incorporate such dependence: Both populations are jointly driven by the same single time-varying index, the two populations are cointegrated, the populations depend on a common age factor, and there is an augmented common factor model in which a population-specific time-varying index is added to the common factor model with the property that it will tend toward a certain constant level over time. Using data from the female populations of Canada and the United States, we show the augmented common factor model is preferred in terms of both goodness-of-fit and ex post forecasting performance. This model is then used to quantify the basis risk in a longevity hedge of 65-year old Canadian females structured using a portfolio of q-forward contracts predicated on U...

Measuring Basis Risk in Longevity Hedges

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual of the compound Poisson model under a threshold dividend strategy. We derive a set of two integro-differential equations satisfied by the expected total discounted dividends until ruin and show how the equations can be solved by using only one of the two integro-differential equations. The cases where profits follow an exponential or a mixture of exponential distributions are then solved and the discussion for the case of a general profit distribution follows by the use of Laplace transforms. We illustrate how the optimal threshold level that maximizes the expected total discounted dividends until ruin can be obtained, and finally we generalize the results to the case where the surplus process is a more general skip-free downwards Levy process.

On a dual model with a dividend threshold

On the joint distribution of surplus before and after ruin under a Markovian regime switching model

Variable annuities are usually sold with a range of guarantees that protect annuity holders from some downside market risk. Although it is common to see variable annuity guarantees written on multiple funds, existing pricing methods are, by and large, based on stochastic processes for one single asset only. In this article, we fill this gap by developing a multivariate valuation framework. First, we consider a multivariate regime-switching model for modeling returns on various assets at the same time. We then identify a risk-neutral probability measure for use with the model under consideration. This is accomplished by a multivariate extension of the regime-switching conditional Esscher transform. We further extend our results to the situation when the guarantee being valued is linked to equity indexes measured in foreign currencies. In particular, we derive a probability measure that is risk-neutral from the perspective of domestic investors. Finally, we illustrate our results with a hypothetical variable annuity guarantee.

Valuing variable annuity guarantees with the multivariate Esscher transform

A fundamental question in the study of mortality-linked securities is how to place a value on them. This is still an open question, partly because there is a lack of liquidly traded longevity indexes or securities from which we can infer the market price of risk. This article develops a framework for pricing mortality-linked securities on the basis of canonical valuation. This framework is largely nonparametric, helping us avoid parameter and model risk, which may be significant in other pricing methods. The framework is then applied to a mortality-linked security, and the results are compared against those derived from other methods.

/pdf/canonical-valuation-of-mortality-linked-securities-5dnffueqmd.pdf

Canonical Valuation of Mortality-Linked Securities

Variable annuities are often sold with guarantees to protect investors from downside investment risk. The majority of variable annuity guarantees are written on more than one asset, but in practice, single-asset (univariate) stochastic investment models are mostly used for pricing and hedging these guarantees. This practical shortcut may lead to problems such as basis risk. In this article, we contribute a multivariate framework for pricing and hedging variable annuity guarantees. We explain how to transform multivariate stochastic investment models into their risk-neutral counterparts, which can then be used for pricing purposes. We also demonstrate how dynamic hedging can be implemented in a multivariate framework and how the potential hedging error can be quantified by stochastic simulations.

https://uwaterloo.ca/center-of-actuarial-excellence/sites/ca.center-of-actuarial-excellence/files/uploads/files/34._paper.pdf

Andrew Cheuk-Yin Ng

Papers

On a dual model with a dividend threshold

On the joint distribution of surplus before and after ruin under a Markovian regime switching model

Valuing variable annuity guarantees with the multivariate Esscher transform

Canonical Valuation of Mortality-Linked Securities

Pricing and Hedging Variable Annuity Guarantees with Multiasset Stochastic Investment Models