Optimal Reinsurance Designs: from an Insurer’s Perspective

The research on optimal reinsurance design dated back to the 1960’s. For nearly half a century, the quest for optimal reinsurance designs has remained a fascinating subject, drawing significant interests from both academicians and practitioners. Its fascination lies in its potential as an effective risk management tool for the insurers. There are many ways of formulating the optimal design of reinsurance, depending on the chosen objective and constraints. In this thesis, we address the problem of optimal reinsurance designs from an insurer’s perspective. For an insurer, an appropriate use of the reinsurance helps to reduce the adverse risk exposure and improve the overall viability of the underlying business. On the other hand, reinsurance incurs additional cost to the insurer in the form of reinsurance premium. This implies a classical risk and reward tradeoff faced by the insurer. The primary objective of the thesis is to develop theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a number of reinsurance models are developed and their optimal reinsurance treaties are derived explicitly. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the most common risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer’s profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer’s empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach

Efficient reinsurance strategies considering counterparty default risk

Insurance companies pursue the objective of increasing their technical profit, but in doing so, they expose themselves to more risks, increasing the variability of their result. In order to balance the potential profitability deriving from the underwriting activity with the related risks, insurers typically resort to reinsurance treaties. In this context arises the problem of finding the optimal treaty which jointly satisfies multiple objectives, typically represented by risk and return metrics. The classical approaches consider only the characteristics of the treaty, neglecting the ones of the reinsurance provider. However, this approach could lead to sub-optimal choices, since it does not consider counterparty default risk. The purpose of this thesis is threefold. Firstly, we extend classical formulas of technical profit of an insurance company to a partial internal model of Solvency II, including the potential default of the reinsurance counterparty. Secondly, we develop a stochastic simulation approach that includes counterparty default risk and potentially other features, for estimating the efficient frontier of reinsurance strategies for a non-life insurance company. Finally, we propose the application of a neural network model for finding the efficient frontier in a multi-objective optimization problem, requiring limited observations and preserving the possibility of deriving the strategies which generate the Pareto front. Numerical applications are performed assuming a multi-line non-life insurer with parameters from the Italian market. The results show the importance of the rating of reinsurers, i.e. counterparty default risk, for the assessment of the optimal reinsurance strategies. Moreover, we show how this risk could become an opportunity in case the reinsurer with high risk offers a discounted price that more than compensate the potential default effect. Finally, the neural network model offers another perspective for determining optimal reinsurance strategies, which can be especially useful in case of high number of potential combinations defining each strategy

Life’s a breach! Ensuring ‘permanence’ in forest carbon sinks under incomplete contract enforcement

As carbon sinks, forests play a critical role in helping to mitigate the growing threat from anthropogenic climate change. Forest carbon offsets transacted between GHG emitters in industrialised countries and sellers in developing countries have emerged as a useful climate policy tool. A model is developed that investigates the role of incentives in forestry carbon sequestration contracts. It considers the optimal design of contracts to ensure landowner participation and hence, permanence in forest carbon sinks in a context of uncertain opportunity costs and incomplete contract enforcement. The optimal contract is driven by the quality of the institutional framework in which the contract is executed, in particular, as it relates to contract enforcement. Stronger institutional frameworks tend to distort the seller’s effort upwards away from the full enforcement outcome. This also leads to greater amounts of carbon sequestered and higher conditional payments made to the seller. Further, where institutions are strong, there is a case for indexing the payment to the carbon market price if permanence is to be ensured. That is, as the carbon price increases, the payment could be raised and vice versa.forest carbon offsets, permanence, contract design, incomplete enforcement

Essays on Credit, Macroprudential Regulation, and Monetary Policy

This dissertation consists of four essays that investigate the economic consequences of frictions in credit markets and the implications for macroprudential and monetary policies. The first essay addresses the following question: How do excessive debt holdings on borrower balance sheets impede economic activity? To address this question, we estimate a non-linear panel threshold model on a large-scale panel data set for euro area non-financial corporates. We account for non-linearities in the debt-investment link and find that excessive corporate leverage negatively affects firm investment if the debt-to-asset ratio exceeds 80 to 85 percent. These non-linearities are economically meaningful and robust across firm size, sector, and profitability, and were aggravated during the European sovereign debt crisis. The second and third essay address the following questions: How does the presence of unregulated shadow banks affect credit markets and the economy? What implications follow for prudential regulation and monetary policy? In the second essay, we develop a quantitative New Keynesian DSGE model for the euro area and estimate the model with full-information Bayesian techniques. We show that changes in bank capital requirements lead to credit leakage between shadow and commercial banks, and that monetary policy can partly mitigate undesired leakage to the shadow banking sector when banking regulation is tightened. In the third essay, I turn to the optimal design of macroprudential regulation when credit is intermediated by traditional banks and unregulated shadow banks. I derive welfare loss functions and show that both cyclical variations and inefficient levels of credit have welfare implications. Regulators face a trade-off related to the composition of credit when deciding on optimal regulation. I find that they lower capital requirements more strongly under optimal policy in response to adverse shocks that trigger credit leakage to risky non-banks. Furthermore, the optimal static level of capital requirements is lower once shadow banks are considered. In the fourth essay, we address the following question: How much do market participants gain from a European Deposit Insurance Scheme (EDIS)? To this end, we develop an open-economy regime-switching DSGE model with bank default and study the effectiveness of EDIS in comparison to national fiscal policies. We find that reinsurance by both national fiscal policy and EDIS is effective in stabilizing the macro economy, even though welfare gains are slightly larger with EDIS and debt-to-GDP ratios rise under fiscal policy reinsurance. We demonstrate that risk-weighted contribution to EDIS are welfare-beneficial and discuss policy trade-offs during the implementation of EDIS

Risk Sharing and Risk Aggregation via Risk Measures

Risk measures have been extensively studied in actuarial science in the guise of premium calculation principles for more than 40 years, and recently, they have been the standard tool for financial institutions in both calculating regulatory capital requirement and internal risk management. This thesis focuses on two topics: risk sharing and risk aggregation via risk measures. The problem of risk sharing concerns the redistribution of a total risk among agents using risk measures to quantify risks. Risk aggregation is to study the worst-case value of aggregate risks over all possible dependence structures with given marginal risks. On the first topic, we address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first establish an inequality for RVaR-based risk aggregation, showing that RVaR satisfies a special form of subadditivity. Then, the Pareto-optimal risk sharing problem is solved through explicit construction. We also study risk sharing in a competitive market and obtain an explicit Arrow-Debreu equilibrium. Robustness and comonotonicity of optimal allocations are investigated, and several novel advantages of ES over VaR from the perspective of a regulator are revealed. Reinsurance, as a special type of risk sharing, has been studied extensively from the perspective of either an insurer or a reinsurer. To take the interests of both parties into consideration, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all such optimal contracts under more general model assumptions. Sufficient conditions that guarantee the existence of the Pareto-optimal contracts are obtained. When the losses of an insurer and a reinsurer are measured by the ES risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. On the second topic, we first study the aggregation of inhomogeneous risks with a special type of model uncertainty, called dependence uncertainty, in individual risk models. We establish general asymptotic equivalence results for the classes of distortion risk measures and convex risk measures under different mild conditions. The results implicitly suggest that it is only reasonable to implement a coherent risk measure for the aggregation of a large number of risks with dependence uncertainty. Then, we bring the well studied dependence uncertainty in individual risk models into collective risk models. We study the worst-case values of the VaR and the ES of the aggregate loss with identically distributed individual losses, under two settings of dependence uncertainty: (i) the counting random variable and the individual losses are independent, and the dependence of the individual losses is unknown; (ii) the dependence of the counting random variable and the individual losses is unknown. Analytical results for the worst-case values of ES are obtained. For the loss from a large portfolio of insurance policies, the asymptotic equivalence of VaR and ES is established, and approximation errors are obtained under the two dependence settings

The Chinese Economic Transformation

"The Chinese Economic Transformation, the 19th volume in the China Update book series, provides an opportunity for young economists to share their views on various issues relating to the Chinese economic transformation. More than half of the contributors to this book are female scholars. Some of the contributors are rising stars in the studies of the Chinese economy and economic transition, and some only recently received their PhDs and are on their way to establishing themselves in the field of China studies. But they have one thing in common: to passionately observe, study and research what is going on in the Chinese economic transformation during the reform period; and, by so doing, make contributions to the policy debates on, and general understanding of, the Chinese economy. The chapters in this volume include an in-depth probe into challenges in capital and credit allocation due to financial friction and policy distortions; investigating the causes of growth slow-down in China and suitable policy responses; the evolution of the household registration system and its impact on off-farm employment and the integration of rural and urban labour markets; the growth, scale and characteristics of nonstandard employment; the development of rural e-commerce and its economic impact; innovation performance of listed enterprises in China; financial services liberalisation and its impact on firms’ performance; financing support schemes for small and medium-sized enterprises (SMEs) and the effect on banks’ credit allocation to SMEs; the potential costs of US–China trade conflict and ways to mitigate them; gender income gap in China’s labour market; causes of blockage of Chinese overseas direct investment and strategies to reduce the probability of encountering obstacles; and the role of state capital in the iron ore boom in Australia. The great variety of topics in this year’s Update allows readers to understand the current shape of the Chinese economy and to think deeply about policies and necessary reforms for future growth and development.

Risk theory and optimal control of Lévy driven processes

Esta tesis contiene tres artículos de investigación con aportes originales. El primer artículo, que coincide con el Capítulo 2, ha sido publicado (Diko and Usabel (17)) en Insurance: Mathematics and Economics, una revista de reconocimiento internacional incluída en JCR. En el citado capítulo se propone un método numérico que permite evaluar la función de utilidad en un marco de proceso de Poisson compuesto con cambio de régimen. Esto supone que los parámetros del modelo de Poisson compuesto pueden variar en el tiempo, gobernados por un proceso de Markov subyacente. Este modelo es una generalización de los procesos que se analizan en la literatura relevante hasta el momento, por tanto el aporte de este capítulo consiste tanto en el desarrollo de un modelo nuevo, capaz de reflejar un entorno económico variable, como en el método de cálculo de cuantías de interés relacionadas con este. Estas incluyen entre otras la probabilidad de la ruina, supervivencia o el déficit medio al producirse la ruina. El Capítulo 3 expone el tratamiento genérico de un problema de control estocástico en el marco de procesos generales de difusión de Lévy. Este tipo de problemas es conocido por su difficultad a la hora de obtener soluciones concretas, ya que las equaciones diferenciales o integro-diferenciales que caracterizan la solución no admiten tratamiento analítico exacto. Habitualmente se aplican métodos numéricos de discretización de tiempo. En esta tesis, se desarrolla un método de solución alternativo que consiste en Erlangizar (dividir en intervalos aleatorios exponenciales) el horizonte temporal establecido con lo que se consigue simplificar la complejidad de las equaciones diferenciales involucradas. Esta transformación lleva a una metodología de aproximación iterativa aplicable a un gran abanico de problemas del area de finanzas y seguros. Los resultados de este capíulo están en el proceso de revisión en Mathematical Finance, una de las revistas de finanzas estocásticas más importantes en el mundo. Por último, el Capíulo 4 ofrece una aplicación de la metodología presentada anteriormente en el marco de solvencia de una compañía de seguros. En este contexto se plantea un problema de decisión sobre la composición de la cartera de inversión optima con el fin de maximizar la utilidad esperada de una cartera sometida a un proceso de riesgo. Aplicando el algoritmo iterativo del Capítulo 3 se calculan las cuantías de interés y se demuestra la rápida convergencia y buenas propiedades del método propuesto. El contenido de este capítulo también representa un aporte original y está actualmente bajo revisión en la revista ASTIN Bulletin, referente principal en el campo de investigación actuarial. En conlusi on, los tres aportes de investigaci on original presentados en esta tesis permiten una aplicación de métodos numéricos para obtener resultados concretos en situaciones que hasta ahora no han sido tratadas en la literaturaChebyshev approximation in risk processes. Optimal control of Lévy diffusions. Risk theory and optimal investmen