We predict mortgage default by applying convolutional neural networks to consumer transaction data. For each consumer we have the balances of the checking account, savings account, and the credit card, in addition to the daily number of transactions on the checking account, and amount transferred into the checking account. With no other information about each consumer we are able to achieve a ROC AUC of 0.918 for the networks, and 0.926 for the networks in combination with a random forests classifier.

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Abstract. In an L2-framework, we study various aspects of stochastic calculus with respect to the centered doubly stochastic Poisson process. We introduce an orthogonal basis via multilinear forms of the value of the random measure and we analyze the chaos representation property. We revise the structure of non-anticipating integration for martingale random fields and in this framework we study non-anticipating differentiation. We present integral representation theorems where the integrand is explicitely given by the non-anticipating derivative.Stochastic derivatives of anticipative nature are also considered: The Malliavin type derivative is put in relationship with another anticipative derivative operator here introduced. This gives a new structural representation of the Malliavin derivative based on simple functions. Finally we exploit these results to provide a Clark-Ocone type formula for the computation of the non-anticipating derivative.

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Abstract. We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modeled via a counting process in line with large part of the literature in credit risk. In order to deal with both cases of inside and partial information we consider the framework of the anticipating calculus of forward integration. This does not require a priori assumptions typical of the framework of enlargement of filtrations. We find necessary and sufficent conditions for the existence of a locally maximizing portfolio of the expected utility at terminal time. We consider a large class of utility functions. In addition we show that the existence of the solution implies the semi-martingale property of the noises driving the stock. Some discussion on unicity of the maxima is included.