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.     

Ethnic-immigrants in founding teams: Effects on prospector strategy and performance in new Internet ventures

We investigated differences in strategy and performance between new Internet ventures with ethnic-immigrant members in the founding team and a matched set of Internet ventures with non-ethnic-non-immigrant team members. Results showed that new ventures with an ethnic-immigrant presence in the founding teams tended to pursue a more aggressive prospector strategy than those with non-ethnic-non-immigrant founding team members. Still, performance of the two groups of ventures was comparable. However, the positive effects of ethnic-immigrant presence on founding teams depended on team size and average age of the founding team members.     

Retirement and transition phenomena in the family purchase process

Research is needed on the family purchase process of retirement‐age couples, because 78 million baby boomers are rapidly approaching retirement age. Both boomers and the retirement‐age couples in this study present special opportunities to marketers through new roles adopted in retirement. This study reports on perceptions of family purchase process participation among retirement‐age couples. Results indicate that transition retirees' family purchase process participation differs from that of post‐transition retirees. This finding has managerial implications for marketers wishing to serve desirable segments of current and future retirement‐age consumers. © 2007 Wiley Periodicals, Inc.     

Financial-market effects of Federal Government budget deficits

Conclusion This paper finds that, for the 30-year period 1955–1984, the federal government budget deficit in the United States had a positive and significant effect on the longer-term nominal interest rate. This finding is at odds with most of the existing literature, which finds federal budget deficits to have no measurable impact upon interest rates in the United States [cf. Evans, 1985; 1987; Hoelscher, 1983; Makin, 1983; Motley, 1983; McMillin, 1986; and Mascaro and Meltzer, 1983]. The difference between the findings here and the findings in these other studies can be traced at least in part to the way in which we specify the deficit variable. That is, we distinguish between thestructural deficit, which approximates theexogenous component of the total deficit, and thecyclical deficit, which represents theendogenous component of the total deficit. By contrast, these other related studies measure the deficit in more aggregated ways, which combine the cyclical deficit with the structural deficit into one variable.     

The Child as Learner, Critic, Inventor, and Technology Design Partner: An Analysis of Three Years of Swedish Student Journals

From Autumn 1998 to Spring 2001, 27 Swedish children (14, at age 5 and 13, at age 7) partnered with an interdisciplinary and international group of researchers supported by a grant from the European Union to create new storytelling technologies for children. After each of the many design activities, children were asked to reflect with drawings and/or writing in a bound paper journal. As the project concluded in the third year, the children's journals were analyzed and four constructs emerged from the data: learner, critic, inventor, and technology design partner. This study examines the motivation for such a research and learning experience, describes the changes in roles we saw represented in our child partners' journals, and suggests possible future directions for educators and technology developers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Real-world comparison of all-cause hospitalizations,hospitalizations due to stroke and major bleeding,and costs for non-valvular atrial fibrillation patients prescribed oral anticoagulants in a US health plan

Aims: To compare the risk of all-cause hospitalization and hospitalizations due to stroke/systemic embolism (SE) and major bleeding, as well as associated healthcare costs for non-valvular atrial fibrillation (NVAF) patients initiating apixaban, dabigatran, rivaroxaban, or warfarin.

Materials and methods: NVAF patients initiating apixaban, dabigatran, rivaroxaban, or warfarin were selected from the OptumInsight Research Database from January 1, 2013–September 30, 2015. Propensity score matching (PSM) was performed between apixaban and each oral anticoagulant. Cox models were used to estimate the risk of stroke/SE and major bleeding. Generalized linear and 2-part models were used to compare healthcare costs.

Results: Of the 47,634 eligible patients, 8,328 warfarin-apixaban pairs, 3,557 dabigatran-apixaban pairs, and 8,440 rivaroxaban-apixaban pairs were matched. Compared to apixaban, warfarin patients were associated with a significantly higher risk of all-cause (hazard ratio [HR]?=?1.30; 95% confidence interval [CI]?=?1.21–1.40) as well as stroke/SE-related (HR?=?1.60; 95% CI?=?1.23–2.07) and major bleeding-related (HR?=?1.95; 95% CI?=?1.60–2.39) hospitalization; rivaroxaban patients were associated with a higher risk of all-cause (HR?=?1.15; 95% CI?=?1.07–1.24) and major bleeding-related hospitalization (HR?=?1.71; 95% CI?=?1.39–2.10); and dabigatran patients were associated with a higher risk of major bleeding hospitalization (HR?=?1.46, 95% CI?=?1.02–2.10). Warfarin patients had significantly higher major bleeding-related and total all-cause healthcare costs compared to apixaban patients. Rivaroxaban patients had significantly higher major bleeding-related costs compared to apixaban patients. No significant results were found for the remaining comparisons.

Limitations: No causal relationships can be concluded, and unobserved confounders may exist in this retrospective database analysis.

Conclusions: This study demonstrated a significantly higher risk of hospitalization (all-cause, stroke/SE, and major bleeding) associated with warfarin, a significantly higher risk of major bleeding hospitalization associated with dabigatran or rivaroxaban, and a significantly higher risk of all-cause hospitalization associated with rivaroxaban compared to apixaban. Lower major bleeding-related costs were observed for apixaban patients compared to warfarin and rivaroxaban patients.     

Enhancing the teaching of introductory economics with a team-based,multi-section competition

The authors describe a unique approach to enhancing student learning at the introductory economics level that utilizes a multi-section, team-based competition. The competition is structured to supplement learning throughout the entire introductory course. Student teams are presented with current economic issues, trends, or events, and use economic tools and theories to comprehensively examine the topics. Students present their analyses in their own sections with one team from each section moving on to compete in an inter-section round. Students are judged on technicality, creativity, and applicability of economic concepts. The competition has the potential to advance students' creativity, collaboration, communication, and critical and analytical thinking skills, while enhancing their ability to apply foundational economic concepts to real-world settings.     

A preliminary look at readmission and mortality among chronically critically ill and other medically complex Medicare patients

Chronically critically ill and other medically complex patients (CCI/MC-Ps) are those who are hospitalized with long-term intensive care needs and require extended periods of hospital-level care. CCI/MC-Ps may be at higher risk for readmission and mortality than other populations due to the severe nature their illnesses. This article examines factors that lead to increased probability of hospital readmission or mortality among CCI/MC Medicare patients. Logistic regression analyses are used to examine mortality and readmissions among the CCI/MC population. Numerous factors including length of stay in the acute hospital, age and gender affect whether a patient is readmitted to the acute care hospital within 90 days of discharge or dies within 60 days following a hospital stay.