T. Artikis

On the unimodality of present-value distributions

Abstract Financial literature in the past appears to have concentrated on developing present-value models, which were essentially deterministic. Even when stochastic formulations are presented, they are often directed towards the establishment of explicit formulate for mean value, variance and, in some cases, semi-variance. Alternative procedures, based on modal values or exact interval estimates for example, require more detailed analytical information regarding the structure of the underlying distribution function. The existence of a unique mode and its associated precision are two important aspects of this problem and both these questions can be addressed by a generalised concept of unimodality. Discounting random cash flows under exponential timing will inevitably lead to a present value, whose distribution is α-unimodal.

A stochastic model for proactive risk management decisions

The analysis of stochastic discounting models provides one of the more powerful tools available for decision-making under conditions of uncertainty. This paper is mainly devoted to the establishment of properties and applications of a particular stochastic discounting model. More precisely, the paper investigates some of the theoretical problems encountered in a stochastic discounting model when assessing mutually exclusive options, and establishes the advantages of considering risk retention in proactive risk-management programs.

Certain selecting and underreporting processes

In this paper, we present a model for promotional advertising and underreporting of incomes. The model is based on the integral part of the product of a discrete random variable with a continuous uniformly distributed random variable.

Analytical and simulation techniques for discounting binomial random sums

Present-value models have often proved invaluable within the financial decision-making process. Such models are becoming increasingly more complex in their stochastic formulation and more sophisticated in their statistical objectives. Recent articles attempt to make exact inferences regarding the probability distribution of the present value. This paper establishes the result that whenever exponential timing is associated with the investment, then @a-unimodality is automatically induced into the present-value distribution irrespective of the selection criteria of the components of that investment. Furthermore, the conditions leading to the familiar (0) unimodality are determined, whereby it often appears to be financially more prudent to delay the timing mechanism than to exercise caution in the selection of the components.

A stochastic integral arising in discounting continuous cash flows and certain transformed characteristic functions

Abstract Transformed characteristic functions are universally recognized as the most powerful tools for investigating distribution functions of complicated stochastic models. The paper is mainly devoted to the establishment of properties and applications of a particular convolution model. More precisely, the paper derives the characteristic function of a convolution model based on a stochastic integral and provides applications of this model in discounting continuous cash flows.

A transformed geometric distribution in stochastic modelling

The analytical concepts of infinite divisibility and (0) unimodality are fundamental to the study of probability distributions in general and to discrete distributions in particular. In this paper, a one-one correspondence is established between these two important properties which will permit any infinitely divisible discrete distribution (with finite mean value) to be transformed into a (0) unimodal discrete distribution. When this transformation is applied specifically to the geometric distribution, the result is a novel distribution, which can be fully and explicitly specified and whose factorial moments can be expressed in closed forms. This transformed geometric distribution is found to apply to underreported geometrically distributed decision processes, embedded renewal processes with logarithmically distributed components, and M/M/1 queues in which the service mechanism has been uniformly improved.

Analytical and computer simulation techniques for a stochastic model arising in discounting continuous uniform cash flows

Present-value models are currently available for both single cash flows and continuous uniform cash flows under uncertain timing. Recent work by the authors has concentrated mainly on establishing theoretical results concerning the conditions under which unimodality will be introduced into the present-value distribution, particularly under exponential timing. Apart from the conventional (0) unimodality, there are two other forms of unimodality available which refer more to the nature of the unimodal behaviour rather than its location. When the timing mechanism operating for a continuous uniform cash flow is modelled by a geometrically distributed sum of exponential inter-assessment times, this paper establishes that the present-value distribution adopts a form of unimodality which is conceptually and structurally distinct from that form of unimodality adopted within the single cash flow analogue. Each present-value distribution will therefore become (0) unimodal under different prevailing economic conditions. One financial implication of these results is that it should be possible to develop coherent funding strategies for selecting a single cash flow option or a continuous uniform cash flow option having due regard to the current financial climate.

Limiting behavior of certain mixtures of distributions

AbstractПустьU — случайная ве личина равномерно распределенная на [0, 1] иY — не зависящая от нее некоторая случ айная величина. В стат ье изучаются свойства ф ункций распределени й случайных величинX=[1−U1/v/Y], построенных поU иY.

Risk management decision making based on random sums incorporating thinned renewal processes in random time

The contribution of stochastic models to the development of risk management as a fundamental organizational discipline has been proved extremely important. It is now generally accepted that stochastic models are the most powerful analytical tools for evaluating the issues and alternatives and charting courses of action of an efficient risk management program. The main purpose of the present paper is to establish properties and applications in risk management decision making related to total risk severity measurement of a new stochastic model, which is based on a thinned stochastic renewal process and the product of two continuous, independent and nonnegative random variables.