Ambiguity on the insurer's side: the demand for insurance

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.

Ambiguity on the insurer's side: the demand for insurance

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.

Unemployment insurance an analysis of optimal mechanisms under aggregate shocks

The purpose of this work is to provide a brief overview of the literature on the optimal design of unemployment insurance systems by analyzing some of the most influential articles published over the last three decades on the subject and extend the main results to a multiple aggregate shocks environment. The properties of optimal contracts are discussed in light of the key assumptions commonly made in theoretical publications on the area. Moreover, the implications of relaxing each of these hypothesis is reckoned as well. The analysis of models of only one unemployment spell starts from the seminal work of Shavell and Weiss (1979). In a simple and common setting, unemployment benefits policies, wage taxes and search effort assignments are covered. Further, the idea that the UI distortion of the relative price of leisure and consumption is the only explanation for the marginal incentives to search for a job is discussed, putting into question the reduction in labor supply caused by social insurance, usually interpreted as solely an evidence of a dynamic moral hazard caused by a substitution effect. In addition, the paper presents one characterization of optimal unemployment insurance contracts in environments in which workers experience multiple unemployment spells. Finally, an extension to multiple aggregate shocks environment is considered. The paper ends with a numerical analysis of the implications of i.i.d. shocks to the optimal unemployment insurance mechanism.

Optimal unemployment insurance for couples

This work analyzes the optimal design of an unemployment insurance program for couples, whose joint search problem in the labor market differ significantly from the problem faced by single agents. We use a version of the sequential search model of the labor market adapted to married agents to compare optimal constant policies for single and married agents, as well as characterize the optimal constant policy when the agency faces single and married agents simultaneously. Our main result is that an agency that gives equal weights to single and married agents will want to give equal utility promises to both types of agents and spend more on the single agent.

The Optimal Capital Structure of Banks: Balancing Deposit Insurance, Capital Requirements and Tax-Advantaged Debt

The capital structure and regulation of financial intermediaries is an important topic for practitioners, regulators and academic researchers. In general, theory predicts that firms choose their capital structures by balancing the benefits of debt (e.g., tax and agency benefits) against its costs (e.g., bankruptcy costs). However, when traditional corporate finance models have been applied to insured financial institutions, the results have generally predicted corner solutions (all equity or all debt) to the capital structure problem. This paper studies the impact and interaction of deposit insurance, capital requirements and tax benefits on a bankÇs choice of optimal capital structure. Using a contingent claims model to value the firm and its associated claims, we find that there exists an interior optimal capital ratio in the presence of deposit insurance, taxes and a minimum fixed capital standard. Banks voluntarily choose to maintain capital in excess of the minimum required in order to balance the risks of insolvency (especially the loss of future tax benefits) against the benefits of additional debt. Because we derive a closed- form solution, our model provides useful insights on several current policy debates including revisions to the regulatory framework for GSEs, tax policy in general and the tax exemption for credit unions.

Impact of dental insurance on adults’ oral health care in Tehran, Iran.

The aim of the present study was to determine relationships between insurance status and utilization of oral health care and its characteristics and to identify factors related to insured patients’ selection of dental clinic or dentist. The study was based on cross-sectional data obtained through phone interviews. The target population included adults in the city of Tehran. Using a two-stage stratified random technique, 3,200 seven-digit numbers resembling real phone numbers were drawn; when calling, 1,669 numbers were unavailable (busy, no answer, fax, line blocked). Of the 1,531 subjects who answered the phone call, 224 were outside the target age (under 18), and 221 refused to respond, leaving 1,086 subjects in the final sample. The interviews were carried out using a structured questionnaire and covered characteristics of dental visits, the respondent’s reason for selecting a particular dentist or clinic and demographic and socio-economic background (gender, age, level of education, income, and insurance status). Data analysis included the Chi-square test, ANOVA, and logistic regression and the corresponding odds ratios (OR). Of all the 1,086 respondents, 57% were women, 62% were under age 35, 46% had a medium and 34% a high level of education, 13% were under the poverty line, and 70% had insurance coverage; 64% with the public, and 6% with a commercial insurance. Having insurance coverage was more likely for women (OR=1.5), for those in the oldest age group (OR=2.0), and for those with a high level of education (OR=2.5). Of those with dental insurance, 54% reported having had a dental visit within the past 12 months ; more often by those with commercial insurance in comparison with public (65% vs. 53% p<0.001). Check-up as the reason for the most recent visit occurred most frequently among those with commercial insurance (28%) compared with those having public insurance (16%) or being non-insured (13%) (p<0.001). Having had two or more dental visits within the past 12 months was most common among insured respondents, when compared with the non-insured (31% vs. 22% p=0.01). The non-insured respondents reported tooth extractions almost twice as frequently as did the insured ones (p<0.001). Of the 726 insured subjects, 60% selected fully out-of-pocket-paid services (FOP), and 53% were unaware of their insurance benefits. Of those who selected FOP, good interpersonal aspects (OR=4.6), being unaware of dental insurance benefits (OR=4.6), and good technical aspects (OR=2.3) as a reason had greater odds of selecting FOP. The present study revealed that dental insurance was positively related to demand for oral health care as well as to utilization of services, but to the latter with a minor extent. Among insured respondents, despite their opportunity to use fully or highly subsidized oral health care services, good interpersonal relationship and high quality of services were the most important factors when an insured patient selected a dentist or a clinic. The present findings indicate a clear need to modify dental insurance systems in Iran to facilitate optimal use of oral health care services to maximize the oral health of the population. A special emphasis in the insurance schemes should be focused on preventive care.

Bank Run Risk and Optimal Reserves

We characterize the optimal reserves, and the generated probability of a bank run, as a function of the penalty imposed by the central bank, the probability of depositors’ liquidity needs, and the return on outside investment opportunities.

Scoping report: current status of index-based insurance in Bangladesh

With current and anticipated increases in magnitude of extreme weather events and a declining consistency in weather patterns, particularly challenging for agriculture, there has been a growing interest in weather index-based insurance (IBI) schemes in Bangladesh. A number of weather index-based insurance products have already been tested and applied across Asia and Africa, with varying degrees of success, as a mechanism to improve livelihood security by enabling vulnerable populations to transfer risk associated with climate change, extreme weather events and other hazards. In the process, these efforts have generated important new knowledge on how these schemes can be designed and implemented for optimal results. However, the practice of index-based insurance is still limited in Bangladesh, and the experience and knowledge generated by the different stakeholders involved needs to be better communicated.

Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility

We characterize the value function of maximizing the total discounted utility of dividend payments for a compound Poisson insurance risk model when strictly positive transaction costs are included, leading to an impulse control problem. We illustrate that well known simple strategies can be optimal in the case of exponential claim amounts. Finally we develop a numerical procedure to deal with general claim amount distributions.

On the design of customized risk measures in insurance, the problem of capital allocation and the theory of fluctuations for Lévy processes

Dans cette thèse, nous étudions quelques problèmes fondamentaux en mathématiques financières et actuarielles, ainsi que leurs applications. Cette thèse est constituée de trois contributions portant principalement sur la théorie de la mesure de risques, le problème de l’allocation du capital et la théorie des fluctuations. Dans le chapitre 2, nous construisons de nouvelles mesures de risque cohérentes et étudions l’allocation de capital dans le cadre de la théorie des risques collectifs. Pour ce faire, nous introduisons la famille des "mesures de risque entropique cumulatifs" (Cumulative Entropic Risk Measures). Le chapitre 3 étudie le problème du portefeuille optimal pour le Entropic Value at Risk dans le cas où les rendements sont modélisés par un processus de diffusion à sauts (Jump-Diffusion). Dans le chapitre 4, nous généralisons la notion de "statistiques naturelles de risque" (natural risk statistics) au cadre multivarié. Cette extension non-triviale produit des mesures de risque multivariées construites à partir des données financiéres et de données d’assurance. Le chapitre 5 introduit les concepts de "drawdown" et de la "vitesse d’épuisement" (speed of depletion) dans la théorie de la ruine. Nous étudions ces concepts pour des modeles de risque décrits par une famille de processus de Lévy spectrallement négatifs.

Unemployment insurance : severance payments and informality in developing countries

We analyze whether the introduction or an increase of unemployment insurance (UI hereafter) beneÖts in developing countries reduces the e§ort made by unemployed workers to secure a new job in the formal sector. We adopt a comparative static approach and we consider the consequences of an increase of current UI beneÖts on unemployed workersídecision variables in this same period, i.e. we focus on an intra-temporal trade-o§, allowing us to assume away moral hazard complications. When there is no informal sector, unemployed workers may devote their time between e§ort to secure a new job in the formal sector and leisure. In the presence of an informal sector, unemployed workers may also devote time to remunerated informal activities. Consequently, the amount of e§ort devoted to secure a new (formal) job generates an opportunity cost, which ceteris paribus, reduces the amount of time devoted to remunerated activities in the informal sector. We show that in the presence of an informal sector, an increase of current UI beneÖts decreases this marginal opportunity cost and therefore unambiguously increases the e§ort undertaken to secure a new job in the formal sector. This intra-temporal e§ect is the only one at play in presence of one-shot UI beneÖts or with severance payments mechanism.

Unemployment insurance in the presence of an informal sector

We study the effect of UI benefits in a typical developing country where the informal sector is sizeable and persistent. In a partial equilibrium environment, ruling out the macroeconomic consequences of UI benefits, we characterize the stationary equilibrium of an economy where policyholders may be employed in the formal sector, short-run unemployed receiving UI benefits or long-run unemployed without UI benefits. We perform comparative static exercises to understand how UI benefits affect unemployed worker´s effort to secure a formal job, their labor supply in the informal sector and leisure time. Our model reveals that an increase in UI benefits generates two opposing effects for the short-run unemployed. First, since search efforts cannot be monitored it generates moral hazard behaviours that lower effort. Second, it generates an income effect as it reduces the marginal cost of searching for a formal job and increases effort.The overall effect is ambiguous and depends on the relative strength of these two effects. Additionally, we show that an increase in UI benefits increases the efforts of long-run unemployed workers. We provide a simple simulation exercise which suggests that the income effect pointed out is not necessarily of second-order importance in comparison with moral hazard strength. This result softens the widespread opinion, usually based on the microeconomic/partial equilibrium argument that the presence of dual labor markets is an obstacle to providing UI in developing countries.

Exploiting satellite-based rainfall for weather index insurance: the challenges of spatial and temporal aggregation

Lack of access to insurance exacerbates the impact of climate variability on smallholder famers in Africa. Unlike traditional insurance, which compensates proven agricultural losses, weather index insurance (WII) pays out in the event that a weather index is breached. In principle, WII could be provided to farmers throughout Africa. There are two data-related hurdles to this. First, most farmers do not live close enough to a rain gauge with sufficiently long record of observations. Second, mismatches between weather indices and yield may expose farmers to uncompensated losses, and insurers to unfair payouts – a phenomenon known as basis risk. In essence, basis risk results from complexities in the progression from meteorological drought (rainfall deficit) to agricultural drought (low soil moisture). In this study, we use a land-surface model to describe the transition from meteorological to agricultural drought. We demonstrate that spatial and temporal aggregation of rainfall results in a clearer link with soil moisture, and hence a reduction in basis risk. We then use an advanced statistical method to show how optimal aggregation of satellite-based rainfall estimates can reduce basis risk, enabling remotely sensed data to be utilized robustly for WII.