Longevity risk and retirement income tax efficiency: A location spending rate puzzle

In this paper we model and solve a retirement consumption problem with differentially taxed accounts, parameterized by longevity risk aversion. The work is motivated by some observations on how Canadians de-accumulate financial wealth during retirement — which seem rather puzzling. While the Modigliani lifecycle model can justify a variety of (pre-tax) de-accumulation or draw down rates depending on risk preferences, the existence of asymmetric taxes implies that certain financial accounts should be depleted faster than others. Our analysis of data from the Survey of Financial Security indicates that Canadian retirees maintain approximately two-thirds of their financial wealth in tax-sheltered accounts and a third in taxable accounts regardless of age. The ratio of taxable to tax-sheltered wealth increases slightly or remains relatively constant depending on household income which is not what one would expect from the lifecycle model. Indeed, using our model we cannot locate a plausible tax function that justifies a constant “account ratio” regardless of age. For example under flat rates taxable accounts should be depleted well before tax-sheltered accounts are ever touched. The account ratio should go to zero quite rapidly in the absence of government mandated withdrawals. We also demonstrate that under progressive income taxes withdrawals are made from both accounts but at different rates depending on account size, pension income and longevity risk preferences. Again, the “account ratio” should eventually decline. We postulate that this sort of behavior is likely due to irrational considerations linked to mental accounting, etc. It remains to be seen whether this will persist over time and under a more careful analysis of Canadian cohorts or if retirees in other countries exhibit the same behavior.     

Spectral collocation method and Darvishi’s preconditionings to solve the generalized Burgers–Huxley equation

In this paper, a numerical solution of the generalized Burgers–Huxley equation is presented. This is the application of spectral collocation method. To reduce roundoff error in this method we use Darvishi’s preconditionings. The numerical results obtained by this method have been compared with the exact solution. It can be seen that they are in a good agreement with each other, because errors are very small and figures of exact and numerical solutions are very similar.     

The tax identity in risk theory — a simple proof and an extension

By linking queueing concepts with risk theory, we give a simple and insightful proof of the tax identity in the Cramér-Lundberg model that was recently derived in Albrecher & Hipp [Albrecher, H., Hipp, C., 2007. Lundberg’s risk process with tax. Blätter der DGVFM 28 (1), 13-28], and extend the identity to arbitrary surplus-dependent tax rates.     

On a compound Poisson risk model with dependence and in the presence of a constant dividend barrier

In this paper, we consider a classical risk process with dependence and in the presence of a constant dividend barrier. The dependence structure between the claim amounts and the interclaim times is introduced through a Farlie–Gumbel–Morgenstern copula. We analyze the expectation of the discounted penalty function and the expectation of the present value of the distributed dividends. For each function, an integro‐differential equation with boundary conditions is derived, and the solution is provided. Finally, we find an explicit solution for each function when the claim amounts are exponentially distributed. We illustrate the impact of the dependence on these two quantities. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling and management of longevity risk: Approximations to survivor functions and dynamic hedging

This paper looks at the development of dynamic hedging strategies for typical pension plan liabilities using longevity-linked hedging instruments. Progress in this area has been hindered by the lack of closed-form formulae for the valuation of mortality-linked liabilities and assets, and the consequent requirement for simulations within simulations. We propose the use of the probit function along with a Taylor expansion to approximate longevity-contingent values. This makes it possible to develop and implement computationally efficient, discrete-time delta hedging strategies using q-forwards as hedging instruments.The methods are tested using the model proposed by Cairns et al. (2006a) (CBD). We find that the probit approximations are generally very accurate, and that the discrete-time hedging strategy is very effective at reducing risk.     

A simplification of Laplace’s method: Applications to the Gamma function and Gauss hypergeometric function

The main difficulties in the Laplace’s method of asymptotic expansions of integrals are originated by a change of variables. We propose a variant of the method which avoids that change of variables and simplifies the computations. On the one hand, the calculation of the coefficients of the asymptotic expansion is remarkably simpler. On the other hand, the asymptotic sequence is as simple as in the standard Laplace’s method: inverse powers of the asymptotic variable. New asymptotic expansions of the Gamma function Γ(z) for large z and the Gauss hypergeometric function ₂F₁(a,b,c;z) for large b and c are given as illustrations. An explicit formula for the coefficients of the classical Stirling expansion of Γ(z) is also given.     

The Hirota’s bilinear method and the tanh–coth method for multiple-soliton solutions of the Sawada–Kotera–Kadomtsev–Petviashvili equation

In this work we derive a new completely integrable dispersive equation. The equation is obtained by combining the Sawada–Kotera (SK) equation with the sense of the Kadomtsev–Petviashvili (KP) equation. The newly derived Sawada–Kotera–Kadomtsev–Petviashvili (SK–KP) equation is studied by using the tanh–coth method, to obtain single-soliton solution, and by the Hirota bilinear method, to determine the N-soliton solutions. The study highlights the significant features of the employed methods and its capability of handling completely integrable equations.     

Energy and Climate Policy Analysis with the Hybrid Bottom-Up Computable General Equilibrium Model SCREEN: The Case of the Swiss CO2 Act

This paper shows how bottom-up activity analyses within a dynamic computable general equilibrium framework can be undertaken for the longer-term analysis of energy and climate policies using the model SCREEN [25]. In particular we demonstrate for the case of Switzerland how the impact of policy measures to reduce the carbon intensity of the energy sector can be assessed with such a model for various socio-economic and environmental dimensions (e.g., C0₂ emissions, GDP, employment, foreign exchange rate). The results can provide valuable insights for the appropriate design of energy or climate policies that allow for the targeted fostering of a more sustainable energy development.