On the Bail-Out Optimal Dividend Problem

This paper studies the optimal dividend problem with capital injection under the constraint that the cumulative dividend strategy is absolutely continuous. We consider an open problem of the general spectrally negative case and derive the optimal solution explicitly using the fluctuation identities of the refracted-reflected L\'evy process. The optimal strategy as well as the value function are concisely written in terms of the scale function. Numerical results are also provided to confirm the analytical conclusions.Comment: To appear in Journal of Optimization Theory and Applications. Keywords: stochastic control, scale functions, refracted-reflected L\'evy processes, bail-out dividend proble

On the optimal dividend problem for a spectrally negative L\'{e}vy process

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes the total expected discounted dividends. Related is the problem where we impose the restriction that ruin be prevented: the beneficiaries of the dividends must then keep the insurance company solvent by bail-out loans. Drawing on the fluctuation theory of spectrally negative L\'{e}vy processes we give an explicit analytical description of the optimal strategy in the set of barrier strategies and the corresponding value function, for either of the problems. Subsequently we investigate when the dividend policy that is optimal among all admissible ones takes the form of a barrier strategy.Comment: Published at http://dx.doi.org/10.1214/105051606000000709 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Interbank network and bank bailouts: Insurance mechanism for non-insured creditors? : [Version 20 Februar 2013]

This paper presents a theory that explains why it is beneficial for banks to engage in circular lending activities on the interbank market. Using a simple network structure, it shows that if there is a non-zero bailout probability, banks can significantly increase the expected repayment of uninsured creditors by entering into cyclical liabilities on the interbank market before investing in loan portfolios. Therefore, banks are better able to attract funds from uninsured creditors. Our results show that implicit government guarantees incentivize banks to have large interbank exposures, to be highly interconnected, and to invest in highly correlated, risky portfolios. This can serve as an explanation for the observed high interconnectedness between banks and their investment behavior in the run-up to the subprime mortgage crisis

Caught between Scylla and Charybdis? Regulating bank leverage when there is rent seeking and risk shifting

Banks face two moral hazard problems: asset substitution by shareholders (e.g., making risky, negative net present value loans) and managerial rent seeking (e.g., investing in inefficient “pet” projects or simply being lazy and uninnovative). The privately-optimal level of bank leverage is neither too low nor too high: It balances effi ciently the market discipline imposed by owners of risky debt on managerial rent-seeking against the asset-substitution induced at high levels of leverage. However, when correlated bank failures can impose significant social costs, regulators may bail out bank creditors. Anticipation of this generates an equilibrium featuring systemic risk in which all banks choose inefficiently high leverage to fund correlated assets. A minimum equity capital requirement can rule out asset substitution but also compromises market discipline by making bank debt too safe. The optimal capital regulation requires that a part of bank capital be unavailable to creditors upon failure, and be available to shareholders only contingent on good performance.Bank capital ; Moral hazard ; Systemic risk

The W,ZW,Z scale functions kit for first passage problems of spectrally negative Levy processes, and applications to the optimization of dividends

First passage problems for spectrally negative L\'evy processes with possible absorbtion or/and reflection at boundaries have been widely applied in mathematical finance, risk, queueing, and inventory/storage theory. Historically, such problems were tackled by taking Laplace transform of the associated Kolmogorov integro-differential equations involving the generator operator. In the last years there appeared an alternative approach based on the solution of two fundamental "two-sided exit" problems from an interval (TSE). A spectrally one-sided process will exit smoothly on one side on an interval, and the solution is simply expressed in terms of a "scale function" $W$ (Bertoin 1997). The non-smooth two-sided exit (or ruin) problem suggests introducing a second scale function $Z$ (Avram, Kyprianou and Pistorius 2004). Since many other problems can be reduced to TSE, researchers produced in the last years a kit of formulas expressed in terms of the "$W,Z$ alphabet" for a great variety of first passage problems. We collect here our favorite recipes from this kit, including a recent one (94) which generalizes the classic De Finetti dividend problem. One interesting use of the kit is for recognizing relationships between apparently unrelated problems -- see Lemma 3. Last but not least, it turned out recently that once the classic $W,Z$ are replaced with appropriate generalizations, the classic formulas for (absorbed/ reflected) L\'evy processes continue to hold for: a) spectrally negative Markov additive processes (Ivanovs and Palmowski 2012), b) spectrally negative L\'evy processes with Poissonian Parisian absorbtion or/and reflection (Avram, Perez and Yamazaki 2017, Avram Zhou 2017), or with Omega killing (Li and Palmowski 2017)

When bigger isn’t better : bailouts and bank behaviour

Lending retail deposits to SMEs and household borrowers may be the traditional role of commercial banks: but banking in Britain has been transformed by increasing consolidation and by the lure of high returns available from wholesale Investment activities. With appropriate changes to the baseline model of commercial banking in Allen and Gale (2007), we show how market power enables banks to collect „seigniorage‟; and how „tail risk‟ investment allows losses to be shifted onto the taxpayer. In principle, the high franchise values associated with market power assist regulatory capital requirements to check risk-taking. But when big banks act strategically, bailout expectations can undermine these disciplining devices: and the taxpayer ends up „on the hook‟- as in the recent crisis. That structural change is needed to prevent a repeat seems clear from the Vickers report, which proposes to protect the taxpayer by a „ring fence‟separating commercial and investment banking

Post crisis challenges to bank regulation

The current crisis has swept aside not only the whole of the US investment banking industry but also the consensual perception of banking risks, contagion and their implication for banking regulation. As everyone agrees now, risks where mispriced, they accumulated in neuralgic points of the financial system, and where amplified by procyclical regulation as well as by the instability and fragility of financial institutions. The use of ratings as carved in stone and lack of adequate procedure to swiftly deal with systemic institutions bankruptcy (whether too-big-to-fail, too complex to fail or too-many to fail). The current paper will not deal with the description and analysis of the crisis, already covered in other contributions to this issue will address the critical choice regulatory authorities will face. In the future regulation has to change, but it is not clear that it will change in the right direction. This may occur if regulatory authorities, possibly influenced by public opinion and political pressure, adopt an incorrect view of financial crisis prevention and management. Indeed, there are two approaches to post-crisis regulation. One is the rare event approach, whereby financial crises will occur infrequently, but are inescapable.