Browse Research
Viewing 3851 to 3875 of 7690 results
1998
This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions
of the second kind (such as the logarithmic utility function).
1998
This article introduces actuaries to the concept of ‘‘copulas,’’ a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Copulas were introduced in 1959 in the context of probabilistic
metric spaces. The literature on the statistical properties and applications of copulas has been developing rapidly in recent years.
1998
The ability of commonly used profitability measures to reflect risk exposure appropriately is evaluated and found lacking. As an alternative, a modern portfolio theory approach, based on utility theory, is recommended. Generalized formulas for calculating risk-adjusted economic values by deriving risk adjustments from certainty equivalents are developed by using the Markowitz expected utility maxim. Practical applications are described.
1998
This paper suggests a possible flexible solution to the time and resource problems of running a large number of stochastic interest rate scenarios, that is, selecting a representative subset. Each interest rate scenario consists of 30 future spot yield curves, in which 12 points are specified on each curve. The distribution of the scenarios is approximated by the subset, and each scenario in the subset has equal weight.
1998
Actuaries, and other managers of uncertainty, identify factors in modeling insurance risks because they believe (1) that these factors affect the outcome of a risk or (2) that the factors can be managed, thus allowing analysts a degree of control over the insurance system. This paper shows how to use a statistical measure, the coefficient of determination, for quantifying the relative importance of a source of uncertainty.
1998
We consider two models in which the logarithm of the price of an asset is a shifted compound Poisson process. Explicit results are obtained for prices and optimal exercise strategies of certain perpetual American options on the asset, in particular for the perpetual put option. In the first model in which the jumps of the asset price are upwards, the results are obtained by the martingale approach and the smooth junction condition.
1998
This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The time of ruin is analyzed in terms of its Laplace transforms, which can naturally be interpreted as discounting. Hence the classical risk theory model is generalized by discounting with respect to the time of ruin.
1998
In this paper I show how methods that have been applied to derive results for the classical risk process can be adapted to derive results for a class of risk processes in which claims occur as a renewal process. In particular, claims occur as an Erlang process.
