Optimal Control of Capital Injections by Reinsurance and Investments

An insurance company, having an initial capital x, cashes premiums continuously and pays claims of random sizes at random times. In addition to that, the company can buy reinsurance or/and invest money into a riskless or risky assets. The company holders are confronted with the problem of taking decisions on a business policy of the company. Thus, a measure for the risk connected with an insurance portfolio is sorely needed. The ruin probability, i.e. the probability that the surplus process becomes negative in finite time, is typically the measure for an insurance company's solvency. However, the ruin probability approach has been criticised among other things for not considering the severity of an insolvency and for ignoring the time value of money. An alternative to measure the risk of a surplus process is to consider the value of expected discounted capital injections, which are necessary to keep the process above zero. Naturally, it raises the question how to minimise this value. If the company holders prefer (or are indifferent) investing tomorrow to investing today, it is optimal to inject capital only when the surplus becomes negative and only as much as is necessary to keep the process above zero. In the first part of this work, we solve the problem of minimising the expected discounted capital injections over all dynamic reinsurance strategies for the classical risk model and its diffusion approximation. In the second part, we extend the concept by adding the possibility of investing money, if the surplus remains positive, into a riskless asset. In these two cases we are able to show the existence and uniqueness of the optimal reinsurance strategy and the value function as the minimising value of expected discounted capital injections. In the third part, we consider the surplus process, where the company holders can invest money into a risky asset modeled as a Black-Scholes model. The forth part extends the setup of the third part by possibility of reinsurance. In the last two cases we solve the problem explicitly only for the case of diffusion approximation. In the classical risk model the concept of viscosity solutions introduced by Crandall and Lions has been used. All the studies are illustrated by simulations, written in Java

Addressing Virtual Work Challenges: Learning From the Field

Companies increasingly rely on virtual teams. Despite numerous studies examining the challenges of geographically dispersed work, the findings are often mixed. The purpose of this article is to identify themes of challenges associated with virtual collaborations based on academic literature and do a gap analysis with industry trends. First, we identify five overarching categories of virtual team challenges based on reviewing the latest trends in the academic literature: trust and relationships, communication and knowledge sharing, perceptions and decision making, leadership, and diversity. Second, we utilize these categories to qualitatively code and analyze the company data from the Fortune Best Places to Work surveys from 2014 to 2017, using the document analysis technique. Our contribution is to identify similarities and differences in scholarly and industry approaches to addressing virtual teamwork challenges and thus highlight opportunities for development and future research

Incivility and Beyond at the Top Management Team Level

Although incivility has been gaining increasing attention in the literature as well as in the industry, academic studies have not examined the effects on top management team (TMT) members. TMT members are different from employees at other levels because they are officers of their organizations who are held to a much higher level of responsibility than those in lower echelons. They are crucial in setting the norms of an organization and have far-reaching influence. This article seeks to uncover the mechanisms that explain what happens when TMT members are targets of uncivil leadership behavior. Semistructured interviews were conducted with 15 TMT members. Findings suggest that TMT members tended to be analytical in their reactions, influencing their responses. This study contributes to the literature on incivility and leadership, filling the gap of addressing such behavior at the TMT level

Deductible imputation in administrative medical claims datasets

Objective: To validate imputation methods used to infer plan-level deductibles and determine which enrollees are in high-deductible health plans (HDHPs) in administrative claims datasets. Data sources and study setting: 2017 medical and pharmaceutical claims from OptumLabs Data Warehouse for US individuals Study design: We impute plan deductibles using four methods: (1) parametric prediction using individual-level spending; (2) parametric prediction with imputation and plan characteristics; (3) highest plan-specific mode of individual annual deductible spending; and (4) deductible spending at the 80th percentile among individuals meeting their deductible. We compare deductibles' levels and categories for imputed versus actual deductibles. Data collection/extraction methods: Not applicable. Principal findings: All methods had a positive predictive value (PPV) for determining high- versus low-deductible plans of ≥87%; negative predictive values (NPV) were lower. The method imputing plan-specific deductible spending modes was most accurate and least computationally intensive (PPV: 95%; NPV: 91%). This method also best correlated with actual deductible levels; 69% of imputed deductibles were within $250 of the true deductible. Conclusions: In the absence of plan structure data, imputing plan-specific modes of individual annual deductible spending best correlates with true deductibles and best predicts enrollees in HDHPs.</p

Optimal Consumption Under Deterministic Income

We consider an individual or household endowed with an initial wealth, having an income and consuming goods and services. The wealth development rate is assumed to be a deterministic continuous function of time. The objective is to maximize the discounted consumption over a finite time horizon. Via the Hamilton–Jacobi–Bellman approach, we prove the existence and the uniqueness of the solution to the considered problem in the viscosity sense. Furthermore, we derive an algorithm for explicit calculation of the value function and optimal strategy. It turns out that the value function is in general not continuous. The method is illustrated by two examples