Abstract
This article investigates a stochastic filtering problem whereby the bor-rower’s hidden credit quality is estimated using ego-network signals. The hidden credit quality process is modeled as a mean reverting Ornstein-Ulehnbeck process. The lender observes the borrower’s behavior modeled as a continuous time diffusion process. The drift of the diffusion process is driven by the hidden credit quality. At discrete fixed times, the lender gets ego-network signals from the borrower and the borrower’s direct friends. The observation filtration thus contains continuous time borrower data augmented with discrete time ego-network signals. Combining the continuous time observation data and ego-network information, we derive filter equations for the hidden process and the properties of the conditional variance. Further, we study the asymptotic properties of the conditional variance when the frequency of arrival of ego-network signals is increased.
Highlights
In this article we propose a filtering technique that uses ego-network signals to estimate a hidden process
We assume that the ego-network signals Zk arrive at equidistant time poin= ts tk, k 0,1, N −1
We have presented stochastic filtering results whereby the hidden credit quality process, modeled as an Ornstein-Ulehnbeck equation drives the drift process of the borrower’s observed behavior score
Summary
In this article we propose a filtering technique that uses ego-network signals to estimate a hidden process. The meeting process is modeled as a random event whose probability is a deterministic function of the population size of the network, large population leading to sparse networks Individuals know their credit type and can observe the credit type of their direct friends (alters) in the network. Our model proposes the inclusion of the ego-network signals Zk into the filtering of the process Xt. The lender’s observation filtration is augmented by the filtration generated by Zk at discrete time points. Existing studies on the mathematical modeling of consumer credit risk include [7] where the authors proposed a continuous time model of a borrower’s credit type. In [11], the author proposed a credit scoring model whereby the borrower’s hidden credit type modeled as a discrete time Markov chain is learned through observing network related variables including reputation, trust and distrust.
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