In this study, we derive an explicit solution for the expected loss of a collateralized loan, focusing on the negative correlation between default intensity and collateral value. Three requirements for the default intensity and the collateral value are imposed. First, the default event can...

In this paper, we analyze model risks separately in pricing models and risk measurement models as follows. (1) In pricing models, model risk is defined as "the risk arising from the use of a model which cannot accurately evaluate market prices, or which is not a mainstream model in the market."...

We compare expected shortfall and value-at-risk (VaR) in terms of consistency with expected utility maximization and elimination of tail risk. We use the concept of stochastic dominance in studying these two aspects of risk measures. We conclude that expected shortfall is more applicable than...

We compare expected shortfall with value-at-risk (VaR) in three aspects: estimation errors, decomposition into risk factors, and optimization. We describe the advantages and the disadvantages of expected shortfall over VaR. We show that expected shortfall is easily decomposed and optimized while...

We evaluate expected and unexpected losses of a bank loan, taking into account the bankfs strategic control of the expected return on the loan. Assuming that the bank supplies an additional loan to minimize the expected loss of the total loan, we provide analytical formulations for expected and...