In this paper, I examine the impact of direct equity injections and troubled asset purchases on bank lending and solvency and analyze how ex ante tighter caps on leverage affect ex post decisions between both interventions. Extending the model of Bachmann (2018) by adding the government as a liquidity supplier, illiquid banks can either sell troubled assets at fire sale prices to collateralized financed liquid banks or to the government. If illiquid banks are forced to sell all troubled assets in order to meet premature withdrawals and the government is left with excess liquidity compared to direct equity injections, they can use these funds to bid up prices. Higher prices reduce future returns on buying illiquid assets and motivate liquid banks´ incentive to lend by crowding out their speculative motive for liquidity hoarding. As a result, troubled asset purchases weakly dominate direct equity injections in terms of lending and solvency, directly amplified by a drop in collateral liquidity. Additionally, regulating illiquid banks ex ante by tighter caps on leverage affects the government's decisions about ex post interventions to effectively stabilize lending and solvency conditions, as the self-reinforcing downward spiral between fire sale prices and collateral liquidity is mitigated. Hence, I find that there exists an inherent nexus between ex ante regulations and ex post interventions. / Series: Department of Economics Working Paper Series

Ce mémoire de maîtrise traite de la théorie de la ruine, et plus spécialement des modèles actuariels avec surplus dans lesquels sont versés des dividendes. Nous étudions en détail un modèle appelé modèle gamma-omega, qui permet de jouer sur les moments de paiement de dividendes ainsi que sur une ruine non-standard de la compagnie. Plusieurs extensions de la littérature sont faites, motivées par des considérations liées à la solvabilité. La première consiste à adapter des résultats d’un article de 2011 à un nouveau modèle modifié grâce à l’ajout d’une contrainte de solvabilité. La seconde, plus conséquente, consiste à démontrer l’optimalité d’une stratégie de barrière pour le paiement des dividendes dans le modèle gamma-omega. La troisième concerne l’adaptation d’un théorème de 2003 sur l’optimalité des barrières en cas de contrainte de solvabilité, qui n’était pas démontré dans le cas des dividendes périodiques. Nous donnons aussi les résultats analogues à l’article de 2011 en cas de barrière sous la contrainte de solvabilité. Enfin, la dernière concerne deux différentes approches à adopter en cas de passage sous le seuil de ruine. Une liquidation forcée du surplus est mise en place dans un premier cas, en parallèle d’une liquidation à la première opportunité en cas de mauvaises prévisions de dividendes. Un processus d’injection de capital est expérimenté dans le deuxième cas. Nous étudions l’impact de ces solutions sur le montant des dividendes espérés. Des illustrations numériques sont proposées pour chaque section, lorsque cela s’avère pertinent. / This master thesis is concerned with risk theory, and more specifically with actuarial surplus models with dividends. We focus on an important model, called the gamma-omega model, which is built to enable the study of both periodic dividend distributions and a non-standard type of ruin. We make several new extensions to this model, which are motivated by solvency considerations. The first one consists in adapting results from a 2011 paper to a new model built on the assumption of a solvency constraint. The second one, more elaborate, consists in proving the optimality of a barrier strategy to pay dividends in the gamma-omega model. The third one deals with the adaptation of a 2003 theorem on the optimality of barrier strategies in the case of solvency constraints, which was not proved right in the periodic dividend framework. We also give analogous results to the 2011 paper in case of an optimal barrier under the solvency constraint. Finally, the last one is concerned with two non-traditional ways of dealing with a ruin event. We first implement a forced liquidation of the surplus in parallel with a possibility of liquidation at first opportunity in case of bad prospects for the dividends. Secondly, we deal with injections of capital into the company reserve, and monitor their implications on the amount of expected dividends. Numerical illustrations are provided in each section, when relevant.

This master's thesis addresses the often overlooked aspect of transaction costs, capital injections, and withdrawals in fund management theory. The research collaboration with Havsfonden, a newly launched quantitative ESG investment fund, aims to enhance their understanding of transaction costs and capital injections while improving their investment model. The thesis includes a comprehensive literature review, the development of a portfolio model that integrates transaction costs and capital injections, and the numerical implementation and testing of the model using MATLAB. Three distinct models focusing on transaction costs, including linear, fixed, and a combination of both, were created. Additionally, three models were developed to examine capital injections, with one based on past performance and the others considering a constant inflow of capital. The findings indicate that our models provide reasonable implementation and effectively capture the nature of capital injections and transaction costs. / Den här uppsatsen ämnar belysa dem många gånger försummade områdena – transaktionskostnader och kapitalinjektioner – inom portföljeteorin. Uppsatsen är i samarbete med Havsfonden, en nylanserad kvantitativ ESG fond, och syftar till att utvidga förståelsen för hur transaktionskostnader och kapitalinjektioner beaktas och kan modelleras. Uppsatsen omfattar en litteraturstudie, ett ramverk som integrerar transaktionskostnader och kapitalinjektioner, samt en numerisk implementation i MATLAB. Tre modeller för transaktionskostnader har utvecklats, vilket omfattar linjära och fasta transaktionskostnader samt en kombinerad version. Därutöver har tre modeller för kapitalinjektioner utvecklas, varav en baseras på portföljens tidigare prestation, medan de andra baseras på ett konstant inflöde av kapital. Resultatet tyder på att modellerna har implementerats riktigt och lyckas skildra dem utmärkande attributen av transaktionskostnader och kapitalinjektioner.