Dynamic term structure modelling with default and mortality risk: new results on existence and monotonicity

Abstract

This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and an integer-valued random measure, generalizing existing approaches in the literature. Then we derive drift conditions which are equivalent to no asymptotic free lunch on the considered market. Existence results are also given. In practice, models possessing a certain monotonicity are favorable and we study general conditions which guarantee this. The setup is illustrated with some examples. Key words. large bond markets, no asymptotic free lunch, default risk, life insurance, inifinite dimensional models, term structure of forward spreads, marked point processes, monotonicity, stochastic partial differential equations arXiv:1306.6267v1 [q-fin.PR]