Probability of ruin with variable premium rate

Abstract

The probability of ruin is investigated under the influence of a premium rate which varies with the level of free reserves. Section 4 develops a number of inequalities for the ruin probability, establishing upper and lower bounds for it in Theorem 4. Theorem 5 gives an expression for the ruin probability, and it is seen in Section 5 that this amounts to a generalization of the ruin probability given by Gerber for the special case of a negative exponential claim size distribution. In that same section it is shown the Lundberg's inequality is not derivable from the generalized theory of Section 4, and this is seen as a drawback of the methods used there. Sections 6 and 7 deal with some special cases, including claim size distributions with monotone failure rates. Section 8 shows that, in contrast with the result for a constant premium that the probability of ruin for zero initial reserve is independent of the claim size distribution, the same result does not hold when the premium rate is allowed to vary. Section 9 gives some comments on the possible effect of “dangerousness” of a claim size distribution on ruin probability.     

Directors' Recommendations on Takeover Bids and the Management of Earnings: Evidence from Australian Takeovers

This article investigates whether Australian companies manage their earnings during takeover bids in a manner consistent with the earnings-management hypothesis. This hypothesis predicts that directors who reject a bid use accrual accounting to increase current earnings, supporting their claim that the bid, relative to earnings, is inadequate. Likewise, directors who accept a bid are predicted to use accrual accounting to decrease current earnings. Overall, the results are not consistent with the earnings-management hypothesis. However, some components of unexpected accruals (our proxy for managed earnings) change in the direction predicted by the earnings-management hypothesis, although these changes are not statistically significant. Using industry adjusted performance measures the conclusion is that unexpected accruals are primarily a manifestation of poor financial performance of target firms in the period leading up to the takeover bid.     

Income Inequality: A Tale of Two Cycles?

Building on previous work, this paper documents the changes in income inequality that have occurred over the past 20 years, right up until the late 1990s. In particular, we are interested in whether or not the path of inequality in the most recent economic cycle differed from that observed in the 1980s. The robustness of the results is investigated using innovative statistical techniques, in an attempt to identify whether or not the observed changes represent real increases or decreases in inequality or whether they can be attributed simply to sampling variation between years. Finally, some preliminary results are presented which attempt to identify some of the reasons underlying the observed trends in income inequality, with a particular focus on the role of the labour market.     

Education: High Potential Not Yet Realized

Knowledge is not easily plucked from the stream of existence and social scientists have to offer the sobering suggestion that while 'What matters is what works', what matters first is how we find out what works. If a blind lurching from one good idea to yet another fashion is to be avoided, the task of finding out what works must be central. The widespread use of systematic monitoring (performance indicators) in education in England provides the kind of data stream needed to make it likely that the occasional dramatic outcome will be noticed, particularly by teachers. This article explains the problems and possibilities of using evidence-based information to improve education.     

Corporate communication of financial risk

This study provides insights on the Financial Risk Management Disclosure (FRMD) patterns of Australian listed resource companies for the 2002–2006 period leading up to and immediately following adoption of the International Financial Reporting Standards (IFRS). Regression analysis demonstrates that corporate governance and capital raisings of firms are significant and positively associated with FRMD patterns. In contrast, overseas stock exchange listing of firms is significantly negatively associated with FRMD patterns. The findings show that the introduction of IFRS changes corporation’s willingness to communicate risk information.     

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.     

Partial anticipation, the flow of information and the economic impact of corporate debt sales

Corporate debt sales have been regarded as 'no news' eventsbecause there is no significant price reaction on average totheir announcement. We explore the hypothesis that this lackof average price reaction to debt sale announcements is explainedby the partial anticipation of debt offers. Theory suggeststhat the demand for debt capital is fundamentally related tochanges in the sources and uses of funds, and we find evidencethat earnings are significantly lower, investment growth issignificantly bigger, and, for some issuers, debt refundingrequirements are significantly greater in the period immediatelyprior to issue than in periods well before and after the issue.We find that this preissue information conditions investors'expectations of issue, thereby affecting the cross-sectionalannouncement date price reaction to debt sales in two ways.First, announcement date price reactions are negative, on average,for unanticipated offers or for those offers where prior informationsuggests that an issue is unlikely. Second, holding the probabilityof issue constant, announcement date price reactions are significantlymore negative for offers that raise more capital than investorsexpected. These results are consistent with cash flow signalingand asymmetric information models of corporate financings.     

Regional vulnerability: The case of East Asia

In a case study of six East Asian economies, we use dynamic factor analysis to estimate a regional component of the exchange market pressure index (EMPI) as a measure of regional financial stress. The extent to which this indicator is explained by regional economic and financial factors is interpreted as regional vulnerability to crisis. We find that regional external liabilities and exuberance in domestic stock and credit markets, as well as the US high-yield spread, were positively correlated with regional vulnerability. Individual country EMPIs are also explained by regional factors, with country-specific factors and trade linkages playing little role.     

International air transportation and economic development

Legislation in 1977 and 1978 effectively deregulated the US domestic air cargo and air passenger transportation industries. International air transportation, largely as the result of the ‘Open Skies’ initiative from 1979 has also gradually been liberalized but progress has been geographically and temporally uneven. This study is concerned with extending the Open Skies concept and in accessing the benefits to the US economy of removing the remaining impediments to the provision of free market services involving, in particular, the full transatlantic market. It initially reviews some of the previous work that has looked at links between industrial location and the quality of international air transportation. It develops a modeling framework to examine the implications of further liberalization on the economies of US regions that currently have limited international services. The work involves a macro-analysis of the impact of European international services for 41 Metropolitan Standard Areas.