## Deterministic Or Stochastic

Traditional actuarial techniques assume a deterministic, usually constant path for returns on assets. There has been some effort to adapt this technique for equity-linked liabilities for example, the Office of the Superintendent of Financial Institutions (OSFI) in Canada mandated a deterministic test for the GMMB under segregated fund contracts. (This mandate has since been superseded by the recommendations of the Task Force on Segregated Funds (SFTF) in 2000.) However, there are problems with...

## Equity Indexed Annuities United States

The U.S. equity-indexed annuity (EIA) offers participation at some specified rate in an underlying index. A participation rate of, say, 80 percent of the specified price index means that if the index rises by 10 percent the interest credited to the policyholder will be 8 percent. The contract will offer a guaranteed minimum payment of the original premium accumulated at a fixed rate a rate of 3 percent per year is common. Fixed surrender values are a standard feature, with no equity linking....

## Share Prices and Dividends

We model separately the dividend yield on stocks, and the force of dividend inflation. The share dividend yield in year t,y(t) is generated using y(t) exp wy 8q(t) + 'y + yn(t) (2.36) yn(t) ayyn(t 1) + ayzy (t) (2.37) So yn(t) is an AR(1) process, independent of the inflation process, zy(t) being a Normal(0,1) white noise series. Clearly E y(t) er E exp(wy 5q(t)) E exp(yn(t))j (2.38) because 8q(t) and yn(t) are independent. E exp(wy 5q(t)) is MSq(wy), where Msq(u) is the moment generating...

## Gmab Example

In this section, we will again work through a single scenario to show how the process described above works in practice. The scenario is set out in a spreadsheet format because this gives a convenient layout for following an individual projection. In practice, spreadsheets are generally not the most suitable framework for a large number of simulations. The main reasons for this are, first, that a spreadsheet approach may be very slow compared with other methods. A spreadsheet approach may,...

## The Wilkie Model Structure

The Wilkie model Wilkie 1986, 1995 was developed over a number of years, with an early version applied to GMMBs in the MGWP Report 1980 and the full version first applied to insurance company solvency by the Faculty of Actuaries Solvency Working Party 1986 . The Wilkie model differs in several fundamental ways from the models covered so far It is a multivariate model, meaning that several related economic series are projected together. This is very useful for applications that require...

## Mcmc For The Rsln Model

The candidate variance is chosen to give an appropriate probability of acceptance. The acceptance probabilities for and depend on the distributions used for the other parameters using those described below, we have acceptance probabilities of around 40 percent for both variables. It is conventional to work with the inverse variance, t a-2, known as the precision. The prior distribution for t1 is the gamma distribution with prior mean 865 and variance 8492 the prior distribution for t2 is gamma...

## Probability Functions for Sn

Using the probability function for Rn, the distribution of the total return index at time n can be calculated analytically. Let Sn represent the total return index at n, assume S0 1, then Sn Rn LN Rn , a Rn where X Rn Rn n - Rn M2 2.27 and a R jR a2 n - R of 2.28 Then, if pn r is the probability function for Rn Fs x Pr Sn lt x XPr Sn x Rn r pn r 2.29 where is the standard normal probability distribution function. Similarly, the probability density function for Sn is fn x XX 4r x-p r Pn r 2.31...