C60 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: GeneralReturn

Equity release contracts allow property owners to receive a financial benefit in exchange for surrendering their real estate to a company. The benefits depend on the life expectancy of owners, the real value of properties, and the rate of interest. These parameters are not the same throughout the years. The aim of the paper is to analyse varying payments of equity release contracts which have already been offered to customers for several years in Poland. A recalculation procedure year by year is proposed applying the actuarial and financial methods. This paper estimates the potential advantages of reverse annuity and reverse mortgage contracts in a changing economic environment. The calculations were made based on actual Polish market data, including the Svensson model of spot interest rate. It is shown that there is considerable scope for increasing retirement income; however, the exact amounts may be unknown. The advantages for customers resulting from changes in parameters and valorization are shown, as well as the risk associated with equity release.

An ageing European population and, therefore, a rising dependency ratio of retirees to the working population, strongly suggests that a pension funding gap will be a key social issue in future. Yet many older people have significant real estate assets that they could access using equity release products. They could sell their assets in exchange for lifelong or temporary monthly payments. Equity release products are relatively new to Poland, but are not yet offered by commercial banks in Czechia and Slovakia. This paper estimates the potential benefits of marriage reverse annuity, and reverse mortgage contracts, using the Svensson model function, and empirical property data from selected Czech, Slovak and Polish cities. The results are also compared to the average pension of inhabitants in the selected cities. It is shown that there is substantial scope for boosting retirement income in all the cases considered, though the precise size of the increase depends on factors such as contract buyers' age and life expectancy, the value of their assets, the payment consequences of a spouse's death, and contract suppliers' pricing policies.

We model the probabilistic structure and cash flows arising from marriage reverse annuity contracts in the case of the joint-life status and the last surviving status. In contrast to the classical approach, we take into consideration that future lifetimes between spouses are dependent. The structure of dependence of the length of spouses' lives is modelled using copulas. The term structure of interest rate is modelled using a time-dependent function. The numerical results are based on actual Polish data covering both the structure of the probabilistic model and the interest rate.

Efficiency and productivity analysis is widely used in health services research. In the paper, two major modelling approaches to efficiency and productivity analysis in health services are evaluated. The first group comprises non-parametric methods based on the theory of mathematical programming, such as data envelopment analysis. The second group originates from econometric analysis of production function. Although the application of quantitative economic analysis in health services is not without problems, the methods discussed are able to help us with identifying best and worst practices within the health systems.