Abstract
We investigate the filtering problem where the borrower’s time varying credit quality process is estimated using continuous time observation process and her (in this paper we refer to the borrower as female and the lender as male) ego-network data. The hidden credit quality is modeled as a hidden Gaussian mean-reverting process whilst the social network is modeled as a continuous time latent space network model. At discrete times, the network data provides unbiased estimates of the current credit state of the borrower and her ego-network. Combining the continuous time observed behavioral data and network information, we provide filter equations for the hidden credit quality and show how the network information reduces information asymmetry between the borrower and the lender. Further, we consider the case when the network information arrival times are random and solve stochastic optimal control problem for a lender having linear quadratic utility function.
Highlights
In this study we consider the problem of stochastic filtering in the presence of network generated information
At discrete time points the observer has access to unbiased signals of the process Xt and of nodes directly linked to the Xt node
We assume that the nodes are individual borrowers in a dynamic social network with the process Xt being borrower’s true credit quality modeled as an OrnsteinUlehnbeck process
Summary
In this study we consider the problem of stochastic filtering in the presence of network generated information. Reference [12] provides a Bayesian dynamic model of relational structure on a latent variable continuous time social network. Some existing studies on consumer credit scoring include [16] whereby the borrower’s credit rating is modelled as a discrete time Markov chain process upon incorporating a latent variable driven by economic conditions. Our work generalizes the SEN-HMM-CSD model in the continuous time continuous state Hidden Markov model direction through the following: inclusion of neighbouring nodes signals in the estimation of credit worthiness, credit limit variability tied to individual’s credit worthiness, and the network ties based on credit type homophily; there is no assumption on a fully connected network model.
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