TL;DR: In this paper, the authors investigate some statistical models for problems of insurance and finance, including Risk Based CapitalNalue at Risk, Asset Liability Management, the distribution of annuities, cash flow evaluations (in the framework of pension funds, embedded value of a portfolio, Asian options) and provisions for claims incurred, but not reported (IBNR).
Abstract: A trend in actuarial finance is to combine technical risk with interest risk. If Y t , t = 1, 2, ... denotes the time-value of money (discount factors at time t) and X t the stochastic payments to be made at time t, the random variable of interest is often the scalar product of these two random vectors V = ΣX t Y t . The vectors X and Y are supposed to be independent, although in general they have dependent components. The current insurance practice based on the law of large numbers disregards the stochastic financial aspects of insurance. On the other hand, introduction of the variables Y 1 , Y 2 ,... to describe the financial aspects necessitates estimation or knowledge of their distribution function. We investigate some statistical models for problems of insurance and finance, including Risk Based CapitalNalue at Risk, Asset Liability Management, the distribution of annuities, cash flow evaluations (in the framework of pension funds, embedded value of a portfolio, Asian options) and provisions for claims incurred, but not reported (IBNR).
TL;DR: In this paper, the authors discuss the relation between the market value of insurance company owners' equity and various components that contribute to that value and the effect of firm insolvency risk on each component of value.
Abstract: In this paper, we discuss the relation between the market value of insurance company owners' equity and various components that contribute to that value. The effect of firm insolvency risk on each component of value is discussed in turn. One natural consequence of this analysis is a conceptual framework for estimating the value of insurance liabilities.
TL;DR: In this paper, the authors consider the nature of life assurance business and suggest the accounting standards appropriate to life assurance companies which would ordinarily result in accounts showing a ‘true and fair view’.
Abstract: The paper first considers concepts of profit in economics, accountancy and the law relating to financial reporting. It then considers the nature of life assurance business and suggests the accounting standards appropriate to life assurance companies which would ordinarily result in accounts showing a ‘true and fair view’. An analysis of the E. C. Insurance Accounts Directive shows that there may be circumstances where its provisions conflict with such standards.The paper considers each of the statutory solvency method, embedded value reporting and the accruals method, and the author finds all of them to be inconsistent with accounting standards and the requirements of the Directive.The author puts forward the ‘Earned Profits’ method, which applies accountancy principles in determining assets and liabilities and takes credit for outstanding revenue matching acquisition costs. This approach is then used in analysing the value of a life assurance company and measuring the rate of return on capital.
TL;DR: In this article, the authors analyze both the term structure of interest and mortality rates role for evaluating a fair value of a life insurance business and compare a traditional deterministic model based on local rules for an Italian balance sheet calculation and a stochastic one based on a diffusion process for both mortality and financial risks.
Abstract: The aim of this paper is to analyze both the term structure of interest and mortality rates role for evaluating a fair value of a life insurance business. In particular, a fair value accounting impact on reserve evaluations is discussed comparing a traditional deterministic model based on local rules for an Italian balance sheet calculation and a stochastic one based on a diffusion process for both mortality and financial risks. As proposed by IAS Board we will separate the embedded derivatives from their host contracts, so the fair value of a traditional life insurance contract would be expressed as the value of four components: the basic contract, the participation option, the option to annuitise and the surrender option. A numerical application to a traditional Italian life insurance policy is discussed.
TL;DR: In this article, the authors apply the extreme value theory to the Constant Proportion Portfolio Insurance (CPPI) and show that the choice of the standard multiple is detailed according to the statistical estimation of the behaviour of extreme variations in rates of assets returns.
Abstract: This paper applies the extreme value theory to the Constant Proportion Portfolio Insurance (CPPI) . In particular, the choice of the standard multiple is detailed according to the statistical estimation of the behaviour of extreme variations in rates of assets returns. Moreover, we introduce the distributions of interarrival times of these extreme movements and show their impact on the portfolio insurance. We illustrate these results on S&P 500 data.