Peer-to-Peer Lending: a Growth-Collapse Model and its Steady-State Analysis

We present a stochastic growth-collapse model for the capital process of a peer-to-peer lending platform. New lenders arrive according to a compound Poisson-type process with a state-dependent intensity function; the growth of the lending capital is from time to time interrupted by partial collapses whose arrival intensities and sizes are also state-dependent. In our model the capital level administered via the platform is the crucial quantity for the generated profit, because the brokerage fee is a fixed (small) fraction of it. Therefore we study its steady-state probability distribution as a key performance measure. In the case of exponentially distributed upward jumps we derive an explicit expression for its probability density, for quite general arrival rates of upward and downward jumps and for certain collapse mechanisms. In the case of generally distributed upward jumps, we derive an explicit expression for the Laplace transform of the steady-state cash level density in various special cases. An alternative model featuring up and down periods and a shot noise mechanism for the downward evolution is also analyzed in steady state.