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

Can “compulsory” annuities provide a fair pension?

This discussion paper finds that since 2002 compulsory annuities no longer provide an actuarially fair pension. Hence annuities are a poor investment giving returns of less than 85% in present value terms. The paper uses a data base of annuity rates collected from MoneyFacts monthly reports since 1994. This includes all products available on the market for Male Only aged 55 to 75 in 5 year increments. The present value of future annuity streams and their resultant moneys worth values (MW) are calculated and analysed, with particular attention to the actuarial aspects. The approach and results are independently confirmed giving a high degree of confidence in the findings. The analysis progresses on from the literature review of recent published work The paper plots historic trends of annuity payout rates and their MW values and highlights some significant characteristics of the annuity market. While annuity rates can be expected to fall as life expectation rises no logical reason can be found to also justify the recent and significant reduction in their MW value below the actuarially fair value of 1.0. This research provides a valuable insight for developing strategies to guide the pensioner when formulating his income drawdown plans, especially in the light of. recent A-day changes

Efficient versus inefficient hedging strategies in the presence of financial and longevity (value at) risk

This paper provides a closed-form Value-at-Risk (VaR) for the net exposure of an annuity provider, taking into account both mortality and interest-rate risk, on both assets and liabilities. It builds a classical risk-return frontier and shows that hedging strategies - such as the transfer of longevity risk - may increase the overall risk while decreasing expected returns, thus resulting in inefficient outcomes. Once calibrated to the 2010 UK longevity and bond market, the model gives conditions under which hedging policies become inefficient

Mortality-Indexed Annuities

Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries, and especially its aggregate form, i.e. the risk of unsystematic changes to general mortality patterns, bears a large potential for accumulative losses for insurers. As obvious risk management tools such as (re)insurance or hedging are less suited to manage an annuity provider’s exposure to aggregate longevity risk, the current paper proposes a new type of life annuities with benefits contingent on actual mortality experience, and it also details actuarial aspects of implementation. Similar adaptations to conventional product design exist in investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience is found in German private health insurance so that the idea is not novel in general, but it is in the context of longevity risk. By not or re-transferring the systematic longevity risk insurers may avoid accumulative losses so that the primary focus in an extensive Monte-Carlo simulation is on the question of whether and to what extent such products are also advantageous for policyholders in contrast to a comparable conventional annuity product

Multi fingered robot hand in industrial robot application using tele-operation

This research focuses on the working and development of wireless robotic hand system. In this research previously developed models have been studied. After analysis of those models, a better approach has been presented in this research. The objective of this research is to design and develop a tele-operated robotic hand system. The robotic hand is intended for providing solutions to industrial problems like robot reprogramming, industrial automation and safety of the workers working in hostile environments. The robotic hand system works in the master slave configuration where Bluetooth is being used as the communication channel for the tele-operation. The master is a glove, embedded with sensors to detect the movement of every joint present in the hand, which a human operator can wear. This joint movement is transferred to the slave robotic hand which will mimic the movement of human operator. The robotic hand is a multi fingered dexterous and anthropomorphic hand. All the fingers are capable of performing flexion, extension, abduction, adduction and hence circumduction. A new combination of pneumatic muscles and springs has been used for the actuation purpose. As a result, this combination reduces the size of the robotic hand by decreasing the number of pneumatic muscles used. The pneumatic muscles are controlled by the opening and closing of solenoid valves. A novel technique has been used in the robotic hand for tendon routing, which gives the ability of independence to all finger joints. The heart of all the control mechanism of the system is mbed microcontroller. The designed system was tested at different module levels. The results show the successful establishment of communication between master and slave at a rate of 10 packets per second, which was sufficient for smooth motion of the system. The amount of torque produced at all the joints in the robotic hand has been presented in this research. The posture tests have been performed in which two fingers were actuated which followed the master. This system has achieved motion of fingers without any tendon coupling problem. The system is able to replace the human industrial workers performing dexterous tasks

Variable Annuity with GMWB: surrender or not, that is the question

Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with Guaranteed Minimum Withdrawal Benefit (GMWB) is an optimal stochastic control problem. The surrender feature available in marketed products allows termination of the contract before maturity, making it also an optimal stopping problem. Although the surrender feature is quite common in variable annuity contracts, there appears to be no published analysis and results for this feature in GMWB under optimal policyholder behaviour - results found in the literature so far are consistent with the absence of such a feature. Also, it is of practical interest to see how the much simpler bang-bang strategy, although not optimal for GMWB, compares with optimal GMWB strategy with surrender option. In this paper we extend our recently developed algorithm (Luo and Shevchenko 2015a) to include surrender option in GMWB and compare prices under different policyholder strategies: optimal, static and bang-bang. Results indicate that following a simple but sub-optimal bang-bang strategy does not lead to significant reduction in the price or equivalently in the fee, in comparison with the optimal strategy. We observed that the extra value added by the surrender option could add very significant value to the GMWB contract. We also performed calculations for static withdrawal with surrender option, which is the same as bang-bang minus the "no-withdrawal" choice. We find that the fee for such contract is only less than 1% smaller when compared to the case of bang-bang strategy, meaning that th "no-withdrawal" option adds little value to the contract.Comment: arXiv admin note: substantial text overlap with arXiv:1410.860

Individual Risk in an Investment-Based Social Security System

This paper examines the risk aspects of an investment-based defined contribution Social Security plan. We focus on the risk after the plan is fully phased in. Individuals deposit a fraction of wages to a Personal Retirement Account (PRA), invest these funds in a 60:40 equity-debt mix, and in a similarly invested annuity at age 67. The value of the assets follows a random walk with mean and variance of a 60:40 equity-debt portfolio over the period 1946-95, a mean log return of 5.5 percent (net of administrative costs of 0.4 percent) and a standard deviation of 12.5 percent. We study he stochastic distributions of this process by doing 10,000 simulations of the 80-year experience of the cohort that reached age 21 in 1998. The resulting annuities are compared to the future defined benefits specified in current law (the benchmark' benefits). With no uncertainty, a 5.5 percent log return would permit the benchmark benefits to be purchased with PRA deposits of 3.1 percent of payroll, only one-sixth of the pay-as-you-go tax needed for the benchmark benefits. Saving a higher share of wages provides a cushion' that protects the individual from the risk of an unacceptably low level of benefits. For example, PRA deposits of 6 percent of wages reduces the probability that the benefits are less than the benchmark to 0.17 and the probability that they are less than 61 percent of the benchmark to 0.05. PRA deposits of 9 percent of wages (half of the tax rate required in a pay-as-you-go system) would substantially reduce these risks. This pure investment-based plan is an extreme case. The investment risk can be reduced further by using a mixed system that combines pay-as-you-go and investment-based components or that makes intergenerational transfers conditional on the performance of stock and bond prices.