Contributions published at Finance and Insurance (Pablo Koch Medina)

The optimal dividend policy problem has been analysed since the 1950s and researches have introduced different settings in order to determine the “best” investments and dividend decisions of a firm. However, few have taken into account current developments on financial markets. In this thesis, managers of companies with the structure of both a classical insurance company (financed through the sale of policies) and a levered investment fund (financed with debt) aim to maximize the value of the firm, measured with a dividend discount model. In order to better reflect the current situation of markets and developments such as: introduction of new regulations after the Global Financial Crisis, ever-increasing size of companies or higher reliance of insurance companies on financial products and investments, additional features – market-consistent valuation and carry costs of capital – are added to existing models and their impact is analyzed. The main conclusion from this thesis is that after the introduction of these modifications, the managers very often choose simpler (than in the existing models) investment strategies or immediately liquidate the firm.

Durch die Globalisierung und den technische Vorschritt sind Unternehmen einer immer stärkeren Vernetzung mit ihrer Umwelt ausgesetzt. Diese Vernetzungen führt im Bereich der Informationstechnologie zu einer neuen, bedrohlichen Risikoart: den Cyberrisiken. Von dieser Bedrohung, welche die Solvenz der betroffenen Unternehmen in Gefahr bringen kann, sind auch immer mehr kleinere und mittlere Unternehmen (KMUs) betroffen. Zur Bekämpfung dieser existentiellen Gefahr für Unternehmen gibt es verschiedene Ansätze, beispielsweise die Weiterbildung der Mitarbeiter und technische Schutzvorkehrungen. Während diese Massnahmen unerlässlich für die Minderung des Risikos sind, lassen sich Attacken dadurch jedoch nicht vollständig verhindern. Um die Bedrohung und die (finanziellen) Folgen weiter zu mindern, bleibt die Option des Risikotransfers, also dem Abschluss einer Versicherung für Cyberrisiken. Diese Arbeit untersucht, ob diese Übertragung der Risiken überhaupt eine Option für KMUs ist, warum viele KMUs noch keine Cyberversicherung haben und ob der Versicherungsmarkt diese Nachfrage mit einem Angebot decken kann. Die vorliegende Arbeit richtet sich daher an Verwaltungsratsmitglieder und Mitglieder des oberen Managements von KMUs, welche die neuen technologischen Risiken und den Umgang mit ihnen besser verstehen wollen, aber auch Personen, die im Versicherungsbereich um den Cyberversicherungsmarkt tätig sind. Dabei wurde die Arbeit von einem betriebswirtschaftlichen (und nicht von einem informationstechnologischen oder versicherungsmathematischen) Standpunkt geschrieben. Anhand der vorhandenen Literatur zeigt sich, dass Schweizer KMUs den Trend der Digitalisierung aufgegriffen haben, sodass sich die Systemarchitektur im Unternehmen stark verändert hat. Das Bewusstsein für die Risiken, die solche Neuerungen mit sich bringen, steigt beim Verwaltungsrat und oberen Management. Die verantwortlichen Führungskräfte beginnen gemäss verschiedenen Studien zu erkennen, dass ein ganzheitliches Risikomanagement mit integrierten, professionellen Cyberrisikomanagementprozessen essentiell ist, um einen grossen Teil der heute existierenden Risiken zu minimieren. Da die finanziellen Schäden von Cyberattacken nicht durch die klassische Betriebshaftpflicht gedeckt sind, steigt das Interesse von Unternehmen an speziell auf Cyberattacken und ihre finanziellen Folgen ausgerichteten Versicherungsprodukten. Die bereits bestehenden Versicherungsprodukte in der Schweiz sind jedoch noch sehr komplex aufgebaut und individuell auf das Unternehmen abgestimmt. Von diesen Angeboten profitieren vor allem Grossunternehmen als First Mover, da es schwierig ist, ein kostengünstiges Cyberprodukt für die Bedürfnisse von KMUs anzubieten. Der Ausblick auf die nächsten Jahre zeigt jedoch, dass rechtliche Änderungen im Cyberbereich – wie die neue Datenschutzgrundverordnung (DSGVO) der Europäischen Union (EU) – sowie die immer grösseren Menge an Daten über Schadensfälle und das immer bessere Verständnis der Cyberrisiken seitens der Unternehmen den Markt für Cyberversicherungspolicen stimulieren werden. Mit dieser erhöhten Relevanz von Datenschutz und dem besseren Verständnis der Risiken bei Versicherungen und Unternehmen wird deshalb erwartet, dass in Zukunft auch Cyberversicherungsprodukte für KMUs entwickelt und von ihnen bezogen werden.

We use a dynamic framework to address the questions: i) when should an insurance firm pay out dividends and raise (costly) capital and ii) when should an insurance firm take (liquid) investment risk. Financial decisions are made by a manager who strives to maximize firm value and operates in the presence of financial frictions and regulatory capital constraints. We show there is a unique pricing measure that is consistent with market prices and a broad ownership base and use it to compute the risk-adjusted net present value of cash flows to shareholders. We describe the capital and dividend strategies of the firm and show that, from a shareholder perspective, investment in risky assets can be value adding. Risky investments may add value by boosting the value of the option to default or, sometimes, by increasing the firm's franchise value.

Diese Arbeit sollte den Fragen nachgehen, mit welchen Problemen sich die Schweizer Altersvorsorge konfrontiert sieht und welche Reformmassnahmen zur Lösung dieser Probleme bestehen. Beantwortet werden sollen diese Fragen durch bereits bestehende Literatur und zusätzlich durch Daten vom Bundesamt für Sozialversicherungen. Diese Literatur und Daten sollen in dieser Arbeit zusammengeführt werden, um einen besseren Überblick über die Problematik der Schweizer Altersvorsorge und die potentiellen Lösungen zu erhalten. Die Schweizer Altersvorsorge lässt sich unterteilen in drei Säulen. Die erste Säule ist die Alters- und Hinterlassenenversicherung (AHV). Die zweite Säule ist die berufliche Vorsorge (BV). Die dritte Säule ist das freiwillige Sparen. In dieser Arbeit wird auf eine thematische Behandlung der dritten Säule verzichtet. Bei der AHV konnte die demografische Entwicklung der Bevölkerung als zentrales Problem identifiziert werden. Das Problem bei der demografischen Entwicklung lässt sich unterteilen in eine steigende Lebenserwartung, eine tiefere Geburtenrate und einem neuen Verhältnis von Jung zu Alt in der Bevölkerung. Bei der BV konnte ein zu hoher Umwandlungssatz, die sinkenden durchschnittlichen Kapitalerträge und die steigende Lebenserwartung als wesentliche Problembereiche identifiziert werden. Mögliche Lösungen bei der AHV wären die Erhöhung des obligatorischen Rentenalters, Rentenkürzungen, Modifikationen des Rentenanpassungsprozesses, die AHV-Beiträge zu erhöhen, die Mehrwertsteuer zu erhöhen, eine nationale Erbschaftssteuer einzuführen oder ökologische Lenkungsabgaben zu erheben. Mögliche Lösungen für die BV wären die Senkung des Mindestumwandlungssatzes, die Anhebung des Rentenalters, die BVG-Beiträge zu erhöhen, höhere Renditen in der BV anzustreben, die Regulierungsdichte zu reduzieren, die Altersgutschriftensätze zu senken, den Koodinationsabzug zu erhöhen oder den Schwellenwert für die Löhne in der BV zu senken. Das langfristige finanzielle Gleichgewicht der Schweizer Altersvorsorge ist durch die genannten Probleme äusserst gefährdet und deshalb besteht ein dringender Reformbedarf. Die sehr schwierige Aufgabe der Politik ist es ein Reformpacket zu schnüren, welches sowohl die langfristige Finanzstabilität der Altersvorsorge wiederherstellt und gleichzeitig auch eine politische Mehrheit im Volk findet und das Referendum übersteht.

This is a summary of the main topics and findings from the Swiss Risk and Insurance Forum 2017. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss past and current developments as well as future perspectives in dealing with asset-liability management for long-term insurance business. Topics include valuation, innovations in insurance products, investment, and modelling aspects.

We solve the problems of mean-variance hedging (MVH) and mean–variance portfolio selection (MVPS) under restricted information. We work in a setting where the underlying price process S is a semimartingale, but not adapted to the filtration G which models the information available for constructing trading strategies. We choose as G=Fdet the zero-information filtration and assume that S is a time-dependent affine transformation of a square-integrable martingale. This class of processes includes in particular arithmetic and exponential Lévy models with suitable integrability. We give explicit solutions to the MVH and MVPS problems in this setting, and we show for the Lévy case how they can be expressed in terms of the Lévy triplet. Explicit formulas are obtained for hedging European call options in the Bachelier and Black-Scholes models.

This paper establishes existence and uniqueness of equilibria in the capital asset pricing model (CAPM) in a setting with incomplete markets in which part of the endowments are non-tradeable. It is shown that in equilibrium, agents are willing to assume aggregate hedgeable risk of the market but will no longer hold fractions of the market portfolio. The paper studies the effects of non-traded endowments on equilibrium asset prices and allocations and establishes a linear pricing formula, a security market line, and conditions for the positivity of asset prices.

We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient to be is radially bounded, i.e. that every ray passing through one of its elements eventually leaves the set. The result is motivated by problems arising in mathematical finance.

We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a linearity-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of financial markets. As a corollary, we obtain existence of a utility maximizer in the frictionless market model, markets with proportional transaction costs and also more general convex costs, like in the case of market impact.

We introduce, in a dynamic-contracting framework with moral hazard, the possibility of recapitalization as an alternative to liquidation when a firm is distressed. This is achieved by considering a risk-averse agent and by allowing (but not requiring) the latter to inject additional capital into the firm when necessary. We show that firm recapitalization may arise in an optimal, long-term contract. As a consequence, we find that there are two mechanisms at a firm’s disposal so as to deal with financial difficulties: one corresponds to a recapitalization process, the other to a liquidation one. The choice of mechanism is based on a cost-benefit analysis.

The allocation of capital and the correspondent costs has become a major focus for business steering and performance measurement in insurance companies. This master's thesis provides insights according to an extended marginal capital allocation method {using a contingent claims approach{ into how profitability rankings of different business lines can be established in a one-period complete market setting. On the basis of that, it is shown in which line the insurer should grow and which to reduce. An application of a simulated portfolio mix evaluation {in imperfect markets{ with performance metrics such as RAROC and EVA when lines of businesses are correlated with the market is performed. According to my analysis, this allows management in insurance to set the scope under what conditions prfitability rankings for subportfolios are relevant. Eventually, implications are brought forward of the conducted performance measurement analysis by demonstrating that by means of an \integrated income statement" approach, EVA is not able to differentiate between earnings from underwriting activities and earnings from investment operations and to establish an exact time reference for those earnings. This implies that EVA may lead to biased profitability rankings.

The concept of \tail risk" is of fundamental importance for quantitative risk management since it refers to those economic scenarios which are particularly relevant from a liability holders' perspective and thus also from a regulatory point of view. Recently, this has been explicitly acknowledged by the Basel Committee on Banking Supervision. However, a clear definition of the notion of \tail risk" is missing in the risk measure literature. This thesis gives a formal definition of \tail risk" and links it to the economic intuition behind the word \tail". Based on this, \tail risk measures" and \tail acceptance sets" are introduced. Then, the notion of a \generator" is used to construct explicit tail risk measures, to investigate their properties and to derive representation results. These findings are complemented by a critical discussion of the introduced concepts. Thereby, the thesis examines and refines the work by Fangda Liu and Ruodu Wang presented in \A Theory for Measures of Tail Risk" (Preprint, 2016).

Any solvency regime for financial institutions should be aligned with the fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. The first objective leads to consider surplus-invariant capital adequacy tests, i.e. tests that do not depend on the surplus of a financial institution. We provide a complete characterization of closed, convex, surplus-invariant capital adequacy tests that highlights an inherent tension between surplus-invariance and the desire to give credit for diversification. The second objective leads to requiring consistency of capital adequacy tests across jurisdictions. Of particular importance in this respect are capital adequacy tests that remain invariant under a change of numéraire. We establish an intimate link between surplus- and numéraire invariant tests.

This is a summary of the main topics and findings from the Swiss Risk and Insurance Forum 2015. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss the past and current developments and necessary next steps for dealing with old-age provision. Topics include the pension funding gap, demographic and societal challenges, the valuation of pension liabilities, economic and regulatory capital models, and the role of financial markets.

We study a continuous-time contracting problem in which size plays a role. The agent may take on excessive risk to enhance short-term gains; doing so exposes the principal to large, infrequent losses. The optimal contract includes size as an instrument: downsizing along the equilibrium path may be necessary so as to preserve incentive compatibility. We characterize the principal's value function and the downsizing process, both of which depend on the nature of the liquidation value. When the latter has fixed and size-dependent components, there is an optimal (endogenous) liquidation size. In the special case where the liquidation value is linear in size, one may describe the solution in size-adjusted terms, which allows for the study of re-investment. The optimal contract is implemented using the full array of financial securities plus debt covenants; holding equity is essential to curb risk taking. Conflicts emerge between classes of security holders and explain phenomena like seniority of claims. Firms for which risk taking is less attractive can afford a higher leverage.

The objective of this book is to give a self-contained presentation to the theory underlying the valuation of derivative financial instruments, which is becoming a standard part of the toolbox of professionals in the financial industry. Although a complete derivation of the Black-Scholes option pricing formula is given, the focus is on finite-time models. Not going for the greatest possible level of generality is greatly rewarded by a greater insight into the underlying economic ideas, putting the reader in an excellent position to proceed to the more general continuous-time theory. The material will be accessible to students and practitioners having a working knowledge of linear algebra and calculus. All additional material is developed from the very beginning as needed. In particular, the book also offers an introduction to modern probability theory, albeit mostly within the context of finite sample spaces. The style of presentation will appeal to financial economics students seeking an elementary but rigorous introduction to the subject; mathematics and physics students looking for an opportunity to become acquainted with this modern applied topic; and mathematicians, physicists or quantitatively inclined economists working in the financial industry.

We derive a result on the limit of certain sequences of principal eigenvalues associated with some elliptic eigenvalue problems. This result is then used to give a complete description of the global structure of the curves of positive steady states of a parameter dependent diffusive version of the classical logistic equation. In particular, we characterize the bifurcation values from infinity to positive steady states. The stability of the positive steady states as well as the asymptotic behaviour of positive solutions is also discussed.