Surplus analysis for variable annuities with a GMDB option

In this paper, we analyze the insurance surplus for a Variable Annuity contract with a Guaranteed Minimum Death Benefit (GMDB) option. Initially, we derive the first two moments of the distribution of the surplus; and subsequently, we develop the whole distribution using a stochastic model which involves an integrated analysis of financial and mortality risk for a portfolio of annuities with GMDB embedded options. We offer a model according which the premium can be modified as per the forecasts of mortality probabilities, interest rate and fund evolution. Moreover, the study enables us to determine the premium that leads to a required probability of insolvency, and so it can be used for an evaluation of the adequacy of solvency. Numerical examples illustrate the results

Forward transition rates

The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions have been proposed. We establish a theoretical framework for the discussion of forward rates. Furthermore, we provide a novel definition with its own logic and merits and compare it with the proposals in the literature. The definition turns the Kolmogorov forward equations inside out by interchanging the transition probabilities with the transition intensities as the object to be calculated.Comment: Revision of manuscript. The manuscript now contains a section on 'Forward-thinking and actuarial practice'. Furthermore, we have corrected typos and re-written certain sentences to improve readability and accurac

The Private Value of Public Pensions

Individual retirement savings accounts are replacing or supplementing public basic pensions. However at decumulation, replacing the public pension with an equivalent private sector income stream may be costly. We value the Australian basic pension by calculating the wealth needed to generate an equivalent payment stream using commercial annuities or phased withdrawals, but still accounting for investment and longevity risks. At age 65, a retiree needs an accumulation of about 8.5 years earnings to match the public pension in real value and insurance features. Increasing management fees by 1% raises required wealth by about one year's earnings. Delaying retirement by 5 years lowers required wealth by about one half year's earnings. Phased withdrawals have money's worth ratios close to 0.5 suggesting that private replacement costs are high.social security; longevity risk; phased withdrawal; stochastic present value

A linear algebraic method for pricing temporary life annuities and insurance policies

We recast the valuation of annuities and life insurance contracts under mortality and interest rates, both of which are stochastic, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations is developed which allows for fast and accurate computation of expected values. Our reformulation of the valuation problem provides a general framework which can be employed to find insurance premiums and annuity values covering a wide class of stochastic models for mortality and interest rate processes. The proposed approach provides a computationally efficient alternative to Monte Carlo based valuation in pricing mortality-linked contingent claims

Managing uncertainty:financial, actuarial and statistical modelling.

present value; Value; Actuarial;

Optimizing the Retirement Portfolio: Asset Allocation, Annuitization, and Risk Aversion

Retirees must draw down their accumulated assets in an orderly fashion so as not to exhaust their funds too soon. We derive the optimal retirement portfolio from a menu that includes payout annuities as well as an investment allocation and a withdrawal strategy, assuming risk aversion, stochastic capital markets, and uncertain lifetimes. The resulting portfolio allocation, when fixed as of retirement, is then compared to phased withdrawal strategies such a "self-annuitization" plan or the 401(k) 'default' pattern encouraged under US tax law. Surprisingly, the fixed percentage approach proves appealing for retirees across a wide range of risk preferences, supporting financial planning advisors who often recommend this rule. We then permit the retiree to switch to an annuity later, which gives her the chance to invest in the capital market and "bet on death." As risk aversion rises, annuities first crowd out bonds in retiree portfolios; at higher risk aversion still, annuities replace equities in the portfolio. Making annuitization compulsory can also lead to substantial utility losses for less risk-averse investors.

Still living with mortality: The longevity risk transfer market after one decade

This paper updates Living with Mortality published in 2006. It describes how the longevity risk transfer market has developed over the intervening period, and, in particular, how insurance-based solutions – buy-outs, buy-ins and longevity insurance – have triumphed over capital markets solutions that were expected to dominate at the time. Some capital markets solutions – longevity-spread bonds, longevity swaps, q-forwards, and tail-risk protection – have come to market, but the volume of business has been disappointingly low. The reason for this is that when market participants compare the index-based solutions of the capital markets with the customized solutions of insurance companies in terms of basis risk, credit risk, regulatory capital, collateral, and liquidity, the former perform on balance less favourably despite a lower potential cost.We discuss the importance of stochastic mortality models for forecasting future longevity and examine some applications of these models, e.g., determining the longevity risk premiumand estimating regulatory capital relief. The longevity risk transfer market is now beginning to recognize that there is insufficient capacity in the insurance and reinsurance industries to deal fully with demand and new solutions for attracting capital markets investors are now being examined – such as longevity-linked securities and reinsurance sidecars