Optimal investment strategies and risk measures in defined contribution pension schemes.

In this paper, we analyse the investment allocation and the downside risk faced by the retiring member of a defined contribution pension scheme, where optimal investment strategies (derived from a dynamic programming approach) have been adopted. The behaviour of the optimal investment strategy is analysed when changing the disutility function and the correlation between the assets. Three different risk measures are considered in analysing the final net replacement ratios achieved by the member: the probability of failing the target, the mean shortfall and a Value at Risk type measure. The replacement ratios encompass the financial and annuitization risks faced by the retiree. We consider the relationship between the risk aversion of the member and these different risk measures in order to understand better the choices confronting different categories of scheme member. We consider the case of a 2 assets portfolio, where the asset returns are correlated and consider the sensitivity of the results to the level of the correlation coefficient.defined contribution pension scheme; optimal investment; downside risk

Controlling the Solvency Interaction Among a Group of Insurance Companies

Pooling of risks is an efficient risk management technique used by large employee benefit schemes of multinational companies to self-insure their retirement and other benefit obligations. This technique forms a basis for formulating a general control theoretic model for the interaction between insurance companies within a pooling network. The objective of these insurance companies is to avoid insolvency yet maintain stable premium and surplus processes. A general control system of equations that is used as a model for the interaction of m insurance companies within the network is first analyzed. An analytic solution is provided. Questions concerning the stability and optimal parameter design for the system are investigated. The special case of two identical companies is analyzed in detail

Controlling the Solvency Interaction Among a Group of Insurance Companies

Pooling of risks is an efficient risk management technique used by large employee benefit schemes of multinational companies to self-insure their retirement and other benefit obligations. This technique forms a basis for formulating a general control theoretic model for the interaction between insurance companies within a pooling network. The objective of these insurance companies is to avoid insolvency yet maintain stable premium and surplus processes. A general control system of equations that is used as a model for the interaction of m insurance companies within the network is first analyzed. An analytic solution is provided. Questions concerning the stability and optimal parameter design for the system are investigated. The special case of two identical companies is analyzed in detail

Modelling and projecting mortality improvement rates using a cohort perspective

We investigate the feasibility of defining, modelling and projecting of (scaled) mortality improvement rates along cohort years-of-birth, that is, using a cohort perspective. This is in contrast to the approach in the literature which has considered mortality improvement rates that are defined by reference to changes in mortality rates over successive calendar years, that is, using a period perspective. In this paper, we offer a comparison of the 2 parallel approaches to modelling and forecasting using mortality improvement rates. Comparisons of simulated life expectancy and annuity value predictions (mainly by the cohort method) using the England & Wales population mortality experiences for males and females under a variety of controlled data trimming exercises are presented and comparisons are also made between the parallel cohort and period based approaches

Mean-variance optimization problems for an accumulation phase in a defined benefit plan

In this paper we deal with contribution rate and asset allocation strategies in a pre-retirement accumulation phase. We consider a single cohort of workers and investigate a retirement plan of a defined benefit type in which an accumulated fund is converted into a life annuity. Due to the random evolution of a mortality intensity, the future price of an annuity, and as a result, the liability of the fund, is uncertain. A manager has control over a contribution rate and an investment strategy and is concerned with covering the random claim. We consider two mean–variance optimization problems, which are quadratic control problems with an additional constraint on the expected value of the terminal surplus of the fund. This functional objectives can be related to the well-established financial theory of claim hedging. The financial market consists of a risk-free asset with a constant force of interest and a risky asset whose price is driven by a Lévy noise, whereas the evolution of a mortality intensity is described by a stochastic differential equation driven by a Brownian motion. Techniques from the stochastic control theory are applied in order to find optimal strategies

Optimal investment strategies and risk measures in defined contribution pension schemes

In this paper, we derive a formula for the optimal investment allocation (derived from a dynamic programming approach) in a defined contribution (DC) pension scheme whose fund is invested in n assets. We then analyse the particular case of n=2 (where we consider the presence in the market of a high-risk and a low-risk asset whose returns are correlated) and study the investment allocation and the downside risk faced by the retiring member of the DC scheme, where optimal investment strategies have been adopted. The behaviour of the optimal investment strategy is analysed when changing the disutility function and the correlation between the assets. Three different risk measures are considered in analysing the final net replacement ratios achieved by the member: the probability of failing the target, the mean shortfall and a value at risk (VaR) measure. The replacement ratios encompass the financial and annuitisation risks faced by the retiree. We consider the relationship between the risk aversion of the member and these different risk measures in order to understand better the choices confronting different categories of scheme member. We also consider the sensitivity of the results to the level of the correlation coefficient

Longevity Basis Risk A methodology for assessing basis risk

This technical report details the methodology developed on behalf of the LBRWG to assess longevity basis risk. A user-guide which provides a high level summary of this report has also been produced. Together these documents form the key outputs of the first phase of a longevity basis risk project commissioned and funded by the IFoA and the LLMA, and undertaken on our behalf by Cass Business School and Hymans Robertson LLP

Optimal investment choices post-retirement in a defined contribution pension scheme

In defined contribution pension schemes, the financial risk is borne by the member. Financial risk occurs both during the accumulation phase (investment risk) and at retirement, when the annuity is bought (annuity risk). The annuity risk faced by the member can be reduced through the “income drawdown option”: the retiree is allowed to choose when to convert the final capital into pension within a certain period of time after retirement. In some countries, there is a limiting age when annuitization becomes compulsory (in UK this age is 75). In the interim, the member can withdraw periodic amounts of money to provide for daily life, within certain limits imposed by the scheme’s rules (or by law). In this paper, we investigate the income drawdown option and define a stochastic optimal control problem, looking for optimal investment strategies to be adopted after retirement, when allowing for periodic fixed withdrawals from the fund. The risk attitude of the member is also considered, by changing a parameter in the disutility function chosen. We find that there is a natural target level of the fund, interpretable as a safety level, which can never be exceeded when optimal control is used. Numerical examples are presented in order to analyse various indices — relevant to the pensioner — when the optimal investment allocation is adopted. These indices include, for example, the risk of outliving the assets before annuitization occurs (risk of ruin), the average time of ruin, the probability of reaching a certain pension target (that is greater than or equal to the pension that the member could buy immediately on retirement), the final outcome that can be reached (distribution of annuity that can be bought at limit age), and how the risk attitude of the member affects the key performance measures mentioned above

Forecasting mortality in subpopulations using Lee-Carter type models: A comparison

The relative performance of multipopulation stochastic mortality models is investigated. When targeting mortality rates, we consider five extensions of the well known Lee–Carter single population extrapolative approach. As an alternative, we consider similar structures when mortality improvement rates are targeted. We use a dataset of deaths and exposures of Italian regions for the years 1974–2008 to conduct a comparison of the models, running a battery of tests to assess the relative goodness of fit and forecasting capability of different approaches. Results show that the preferable models are those striking a balance between complexity and flexibility

Valuation of guaranteed annuity conversion options

In this note we introduce a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain deferred annuity pension-type contracts in the UK. The valuation approach is based on the similarity between the payoff structure of the contract and a call option written on a coupon-bearing bond. The model makes use of a one-factor Heath–Jarrow–Morton framework for the term structure of interest rates. Numerical results are investigated and the sensitivity of the price of the option to changes in the key parameters is also analyzed