Risk Management with Non-Convex and Non-Monotone Preferences

This thesis studies two types of problems, the theory of risk functionals and the risk sharing problem. We put a special focus on a class of non-monotone law-invariant risk functionals, called the signed Choquet integrals. The contribution can be seen as three portions. The first portion of this thesis contains various results on signed Choquet integrals. A functional characterization via comonotonic additivity is established, along with some theoretical properties including six equivalent conditions for a signed Choquet integral to be convex. We proceed to address two practical issues currently popular in risk management, namely, robustness (continuity) issues and risk aggregation with dependence uncertainty, for signed Choquet integrals. Our results generalize in several directions those in the literature of risk functionals. From the results obtained in this chapter, we see that many existing elegant mathematical results in the theory of risk measures hold for the general class of signed Choquet integrals; thus they do not rely on the assumption of monotonicity. In the second portion, we analyze the “convex level sets” (CxLS) property of risk functionals, which is a necessary condition for the notions of elicitability, identifiability, and backtestability, popular in the recent statistics and risk management literature. We put the CxLS property in the context of multi-dimensional risk functionals. We obtain two main analytical results in dimension one and dimension two, by characterizing the CxLS property of all one-dimensional signed Choquet integrals, and that of all two-dimensional signed Choquet integrals with a quantile component. Using these results, we proceed to show that a comonotonic-additive coherent risk measure is co-elicitable with a Value-at- Risk if and only if it is a convex combination of the mean and the corresponding Expected Shortfall. The new findings generalize several results in the recent literature and partially answer an open question on the characterization of multi-dimensional elicitability. In the third portion, we study a risk sharing problem. Unlike classic risk sharing problems based on expected utilities or convex risk measures, quantile-based risk sharing problems exhibit two special features. First, quantile-based risk measures (such as the Value-at-Risk) are often not convex, and second, they ignore some part of the distribution of the risk. These features create technical challenges in establishing a full characterization of optimal allocations, a question left unanswered in the literature. In this paper, we address the issues on the existence and the characterization of (Pareto-)optimal allocations in quantile-based risk sharing problems. It turns out that negative dependence, mutual exclusivity in particular, plays an important role in the optimal allocations, in contrast to positive dependence appearing in classic risk sharing problems. As a by-product of our main finding, we obtain some results on the optimization of the Value-at-Risk and the Expected Shortfall

Cash transfers in an epidemic context : the interaction of formal and informal support in rural Malawi

This paper investigates the short-run consumption expenditure dynamics and the interaction of public and private arrangements of ultra-poor and labor-constrained households in Malawi using an original dataset from the Mchinjii social cash transfer pilot project (one of the first experiments of social protection policies based on unconditional cash transfers in Sub-Saharan Africa). The authors exploit the unique source of exogenous variation provided by the randomized component of the program in order to isolate the effect of cash transfers on consumption expenditures as well as the net crowding out effect of cash transfers on private arrangements. They find a statistically significant reduction effect on the level of consumption expenditures for those households receiving cash transfers, thus leading to the rejection of the perfect risk sharing hypothesis. Moreover, by looking at the effects of cash transfers on private arrangements in a context characterized by imperfect enforceability of contracts and by a social fabric heavily compromised by high HIV/AIDS rates, the analysis confirms the presence of crowding out effects on private arrangements when looking at gifts and (to a lesser extent) remittances, while informal loans seem to be completely independent from the cash transfer's reception. From a policy perspective, the paper offers a contribution to the evaluation of the very recent wave of social protection policies based on (unconditional) cash transfers in Sub-Saharan Africa, suggesting that there might be an important role for public interventions aimed at helping households to pool risk more effectively.Safety Nets and Transfers,Rural Poverty Reduction,Labor Policies,Services&Transfers to Poor,Debt Markets

Consumption smoothing and vunerability in Russia

Applying bootstrapped quantile regression to the Russian Longitudinal Monitoring Survey (RLMS) data, we examine the channels through which individuals experience and seek to cope with changes in consumption. We find that married individuals living in small households, with educated heads in urban areas are better equipped to smooth consumption. Investigating the impact of idiosyncratic shocks, we find that the labour market is an important transmission mechanism allowing households to smooth their consumption but also exposing them to risk, mainly through job loss. Outside of pension payments the formal social safety net does not facilitate consumption smoothing, thus heightening the importance of informal coping institutions. It transpires that both support from relatives/friends and home production act as important insurance mechanisms for the most vulnerable

Consumption Smoothing and Vulnerability in Russia

Applying bootstrapped quantile regression to the Russian Longitudinal Monitoring Survey (RLMS) data, we examine the channels through which individuals experience and seek to cope with changes in consumption. We find that married individuals living in small households, with educated heads in urban areas are better equipped to smooth consumption. Investigating the impact of idiosyncratic shocks, we find that the labour market is an important transmission mechanism allowing households to smooth their consumption but also exposing them to risk, mainly through job loss. Outside of pension payments the formal social safety net does not facilitate consumption smoothing, thus heightening the importance of informal coping institutions. It transpires that both support from relatives/friends and home production act as important insurance mechanisms for the most vulnerable.http://deepblue.lib.umich.edu/bitstream/2027.42/64415/1/wp885.pd

Intergenerational risk sharing and labour supply in collective funded pension schemes with defined benefits

Collective funded pension schemes with defined benefits (DB) raise welfare through intergenerational risk sharing, but may lower welfare through distortion of the labour-leisure decision. This paper compares the welfare gains with the welfare losses. In many countries, collective funded pension schemes with defined benefits (DB) are being replaced by individual schemes with defined contributions. Collective funded DB pensions may indeed reduce social welfare when the schemes feature income-related contributions that distort the labour-leisure decision. However, these schemes also share risks between generations and�add to welfare if these risks cannot be traded on capital markets. Do�the�gains outweigh the losses? For answering this question, we adopt a two-period overlapping-generations model for a small open economy with risky returns to equity holdings. We derive analytically that the gains dominate the losses for the case of Cobb-Douglas preferences between labour and leisure. Numerical simulations for the more general CES case confirm these findings, which also withstand a number of other model modifications (like the introduction of a short-sale constraint for households and the inclusion of a labour income tax). These results suggest that collective funded schemes with well-organized risk sharing are preferable over individual schemes, even if labour market distortions are taken into account.

Crime and Social media

Purpose-The study complements the scant macroeconomic literature on the development outcomes of social media by examining the relationship between Facebook penetration and violent crime levels in a cross-section of 148 countries for the year 2012. Design/methodology/approach-The empirical evidence is based on Ordinary Least Squares (OLS), Tobit and Quantile regressions. In order to respond to policy concerns on the limited evidence on the consequences of social media in developing countries, the dataset is disaggregated into regions and income levels. The decomposition by income levels included: low income, lower middle income, upper middle income and high income. The corresponding regions include: Europe and Central Asia, East Asia and the Pacific, Middle East and North Africa, Sub-Saharan Africa and Latin America. Findings-From OLS and Tobit regressions, there is a negative relationship between Facebook penetration and crime. However, Quantile regressions reveal that the established negative relationship is noticeable exclusively in the 90th crime decile. Further, when the dataset is decomposed into regions and income levels, the negative relationship is evident in the Middle East and North Africa (MENA) while a positive relationship is confirmed for sub-Saharan Africa. Policy implications are discussed. Originality/value- Studies on the development outcomes of social media are sparse because of a lack of reliable macroeconomic data on social media. This study primarily complemented three existing studies that have leveraged on a newly available dataset on Facebook

Coping with economic shocks: Consumption Smoothing and the 1998 Russian Financial Crisis

Applying quantile regression techniques to Russian data we investigate the channels through which individuals experience changes in their well being. We find that married individuals in non-rural households with university-educated heads are less vulnerable to severe welfare shocks. For the most vulnerable individuals the labour market plays a key role in transmitting the effects of aggregate shocks through the unemployment channel whereas those individuals able to maintain their employment status are more able to cope with economic shocks. While increases in pension payments help individuals to cope with shocks, it transpires that vulnerable individuals rely more broadly on the support of relatives and the produce of their garden plots and dachas

Measuring association via lack of co-monotonicity: the LOC index and a problem of educational assessment

Measuring association, or the lack of it, between variables plays an important role in a variety of research areas, including education, which is of our primary interest in this paper. Given, for example, student marks on several study subjects, we may for a number of reasons be interested in measuring the lack of co-monotonicity (LOC) between the marks, which rarely follow monotone, let alone linear, patterns. For this purpose, in this paper we explore a novel approach based on a LOC index, which is related to, yet substantially different from, Eckhard Liebscher's recently suggested coefficient of monotonically increasing dependence. To illustrate the new technique, we analyze a data-set of student marks on mathematics, reading and spelling

Taxes and Entrepreneurial Activity: Theory and Evidence for the U.S.

Entrepreneurial activity is presumed to generate important spillovers, potentially justifying tax subsidies. How does the tax law affect individual incentives? How much of an impact has it had in practice? We first show theoretically that taxes can affect the incentives to be an entrepreneur due simply to differences in tax rates on business vs. wage and salary income, due to differences in the tax treatment of losses vs. profits through a progressive rate structure and through the option to incorporate, and due to risk-sharing with the government. We then provide empirical evidence using U.S. individual tax return data that these aspects of the tax law have had large effects on actual behavior.