Search

In the Black-Scholes model, any dividends on stocks are paid continuously, but in reality dividends are always paid discretely, often after some announcement of the amount of the dividend. It [...]

Insurance companies and banks regularly have to face stress tests performed by regulatory instances. To model their investment decision problems that includes stress scenarios, we propose the worst-case portfolio approach. Thus, the resulting optimal portfolios are already stress test prone by construction. A central issue of the worst-case portfolio approach is that neither the time nor the order of occurrence of the stress scenarios are known. Even more, there are no probabilistic assumptions regarding the occurrence of the stresses. By defining the relative worst-case loss and introducing the concept of minimum constant portfolio processes, we generalize the traditional concepts of the indifference frontier and the indifference-optimality principle. We prove the existence of a minimum constant portfolio process that is optimal for the multi-stress worst-case problem. As a main result we derive a verification theorem that provides conditions on Lagrange multipliers and nonlinear ordinary differential equations that support the construction of optimal worst-case portfolio strategies. The practical applicability of the verification theorem is demonstrated via numerical solution of various worst-case problems with stresses. There, it is in particular shown that an investor who chooses the worst-case optimal portfolio process may have a preference regarding the order of stresses, but there may also be stress scenarios where he/she is indifferent regarding the order and time of occurrence. [ABSTRACT FROM AUTHOR]

Although variational autoencoders (VAE) are successfully used to obtain meaningful lowdimensional representations for high-dimensional data, the characterization of critical points of the loss function for general observation models is not fully understood. We introduce a theoretical framework that is based on a connection between fi-VAE and generalized linear models (GLM). The equality between the activation function of a fi-VAE and the inverse of the link function of a GLM enables us to provide a systematic generalization of the loss analysis for fi-VAE based on the assumption that the observation model distribution belongs to an exponential dispersion family (EDF). As a result, we can initialize fi-VAE nets by maximum likelihood estimates (MLE) that enhance the training performance on both synthetic and real world data sets. As a further consequence, we analytically describe the auto-pruning property inherent in the fi-VAE objective and reason for posterior collapse. [ABSTRACT FROM AUTHOR]

We consider two aspects of Vasicek interest rate models arising from chance-risk classification of German pension products. First, we show that the two-factor Vasicek model can explain significantly more effects that are observed at the market than its one-factor variant. Among them are humped shapes independent of the interest rate level and the occurrence of dipped yield curves. We further introduce a general change of measure framework for the Monte Carlo simulation of the Vasicek model under a subjective measure. In chance-risk classification it can then be used to avoid the occurrence of a far too high frequency of inverse yield curves with growing time. [ABSTRACT FROM AUTHOR]