A diffusion approximation for the ruin function of a risk process with compounding assets

Abstract

The traditional theory of collective risk is concerned with fluctuations in the capital reserve {Y(t): t ?O} of an insurance company. The classical model represents {Y(t)} as a positive constant x (initial capital) plus a deterministic linear function (cumulative income) minus a compound Poisson process (cumulative claims). The central problem is to determine the ruin probability ψ(x) that capital ever falls to zero. It is known that, under reasonable assumptions, one can approximate {Y(t)} by an appropriate Wiener process and hence ψ(.) by the corresponding exponential function of (Brownian) first passage probabilities. This paper considers the classical model modified by the assumption that interest is earned continuously on current capital at rate β > O. It is argued that Y(t) can in this case be approximated by a diffusion process Y*(t) which is closely related to the classical Ornstein-Uhlenbeck process. The diffusion {Y*(t)}, which we call compounding Brownian motion, reduces to the ordinary Wiener process when β = O. The first passage probabilities for Y*(t) are found to form a truncated normal distribution, which approximates the ruin function ψ(.) for the model with compounding assets. The approximate expression for ψ(.) is compared against the exact expression for a special case in which the latter is known. Assuming parameter values for which one would anticipate a good approximation, the two expressions are found to agree extremely well over a wide range of initial asset levels.     

Experimental Evidence on Alternative Environmental Valuation Methods

Experimental methods are central to assessments of environmental valuation approaches that are operationally meaningful. Existing lab experiments focus attention sharply on the neglect of hypothetical bias. They also offer constructive solutions to correct this bias, and beg for validation in field experiments.     

OPTIMAL GROWTH STRATEGIES FOR PASTORAL FIRMS IN THE QUEENSLAND BRIGALOW SCHEME

The Brigalow Scheme has been one of Australia's largest dryland development projects since World War II. Large sums of private and public capital have been invested to create 247 new farm firms. Planning the development of these new properties is a complex task. A simulation model of the typical block in Area III of the Brigalow Scheme has been constructed and used to evaluate experimentally the financial performance of various growth strategies. Use of a conjugate directions search procedure with this model has allowed growth strategies to be identified which maximize net worth subject to a low risk of financial failure. These strategies are compared with development programmes which have already been implemented. Significant conclusions are reached both with respect to future management strategies and future land development policies. Methodological advances incorporated in the simulation model are also discussed.     

Returns to scale and externalities in the consumption and investment sectors

Using data on US manufacturing, I estimate internal returns to scale and external effects for the consumption and investment sectors. I construct panels of data at the industry level and use results of gross output production function estimation to derive implied estimates in a value added specification. For the investment sector, returns to scale appear to be slightly increasing, with evidence of a positive external effect. For consumption, the evidence indicates decreasing to constant returns to scale. I discuss the implications of these results for the empirical plausibility of indeterminacy in recent multi-sector models of the business cycle.     

Is a Long‐term Business Relationship an Implied Contract? Two Views of Relationship Disengagement*

ABSTRACT Current knowledge of business‐to‐business relationship dissolution centres upon definitions of relationship dissolution, models of dissolution, antecedents for dissolution, and dissolution strategies. In this paper an empirical case example of a terminated business relationship in the aftermath stage of the dissolution process is presented. William Baird sued Marks and Spencer for £53.6 m for breach of contract. The relationship between the actors was long‐term, exclusive, and involved substantial investment in specific assets. There was no written contract in place, yet one actor considered that the relationship was equal to an implied contract. The contribution of the paper is to discuss the possibility for legal redress using the transaction cost economics, relational contracting, and industrial networks literatures.     

Analyzing the Analysts: Career Concerns and Biased Earnings Forecasts

We examine security analysts' career concerns by relating their earnings forecasts to job separations. Relatively accurate forecasters are more likely to experience favorable career outcomes like moving up to a high-status brokerage house. Controlling for accuracy, analysts who are optimistic relative to the consensus are more likely to experience favorable job separations. For analysts who cover stocks underwritten by their houses, job separations depend less on accuracy and more on optimism. Job separations were less sensitive to accuracy and more sensitive to optimism during the recent stock market mania. Brokerage houses apparently reward optimistic analysts who promote stocks.     

WEALTH DISTRIBUTION AND INVESTMENT INCOME IN BRITAIN*

This paper examines two different approaches to the estimation of the size distribution of wealth. The first section describes new estimates for the distribution in Britain in 1968 using the estate method and discusses the sensitivity of the results to the main assumptions. The second section presents preliminary estimates using the investment data, a method which has not been widely used. In the final section the results obtained for the upper tail of the distribution from the two methods are compared.