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We propose a novel framework for credit risk modeling, where default or failure information and rating or expert information are jointly incorporated in the model. These sources of information are modeled as response variables in a multivariate ordinal regression model estimated by a composite likelihood procedure. The proposed framework provides probabilities of default conditional on the rating information observed at the beginning of a predetermined period and is able to account for missing failure or credit rating information. Our approach is, to the best of our knowledge, the first that consistently combines failure-prediction models, where default indicators are used as responses, with so-called shadow rating models, where the responses are estimates of default probabilities usually derived from the leading credit rating agencies. In our empirical analysis we apply the proposed framework to a data set of US firms over the period from 1985 to 2014. Different sets of financial ratios constructed from financial statements and market information are selected as bankruptcy predictors in line with the standard literature in failure-prediction modeling. We find that the joint model of failures and credit ratings outperforms state-of-the-art failure-prediction models and shadow rating approaches in terms of prediction accuracy and discriminatory power

We consider optimal consumption and (strategic) asset allocation of an investor with uncertain lifetime. The problem is solved using a multi-stage stochastic linear programming (SLP) model to be able to generalize the closed-form solution obtained by Richard (1975). We account for aspects of the application of the SLP approach which arise in the context of life-cycle asset allocation, but are also relevant for other problems of similar structure. The objective is to maximize the expected utility of consumption over the lifetime and of bequest at the time of death of the investor. Since we maximize utility (rather than other objectives which can be implemented more easily) we provide a new approach to optimize the breakpoints required for the linearization of the utility function. The uncertainty of the problem is described by discrete scenario trees. The model solves for the rebalancing decisions in the first few years of the investor's lifetime, accounting for anticipated cash flows in the near future, and applies Richard's closed-form solution for the long, subsequent steady-state period. In our numerical examples we first show that available closed-form solutions can be accurately replicated with the SLP-based approach. Second, we add elements to the problem specification which are usually beyond the scope of closed-form solutions. We find that the SLP approach is well suited to account for these extensions of the classical Merton setting.