Optimal risk sharing with translation invariant recursive utility for jump-diffusions

Abstract

We consider optimal risk sharing where agents have preferences represented by translation invariant recursive utility. The dynamics in continuous time is driven by diffusion processes and a random jump measure. The model has some appealing features compared to the scale invariant version. Economic effects of sudden events, like catastrophes or pandemics, can be interpreted and separated from ordinary shocks to the economy. Unlike the scale invariant version, this model allows for a treatment of heterogeneous preferences, and consequently optimal risk sharing at a general and basic level. A new endogenous variable, a traded security, enters via the preference structure, affecting the key relations between agents. We also implement a stock market in this setting, and derive a consumption based capital asset model. A catastrophe-insurance forward contract is analyzed as an application of our general model, where the jump part is priced and plays the essential role.