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Defaultable bonds with an infinite number of Lévy factors

Jacek Jakubowski, Mariusz Niewęgłowski (2010)

Applicationes Mathematicae

A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Lévy factors is considered. The setting includes rating migrations driven by a Markov chain. All basic types of recovery are investigated. We formulate necessary and sufficient conditions (generalized HJM conditions) under which the market is arbitrage-free. Connections with consistency conditions are discussed.

Defaultable game options in a hazard process model.

Bielecki, Tomasz R., Crépey, Stéphane, Jeanblanc, Monique, Rutkowski, Marek (2009)

Journal of Applied Mathematics and Stochastic Analysis

Diffusion processes and second order elliptic operators with singular coefficients for lower order terms.

Z.Q. Chen, Z. Zhao (1995)

Mathematische Annalen

Doubly reflected BSDEs with call protection and their approximation

Jean-François Chassagneux, Stéphane Crépey (2014)

ESAIM: Probability and Statistics

We study the numerical approximation of doubly reflected backward stochastic differential equations with intermittent upper barrier (RIBSDEs). These denote reflected BSDEs in which the upper barrier is only active on certain random time intervals. From the point of view of financial interpretation, RIBSDEs arise as pricing equations of game options with constrained callability. In a Markovian set-up we prove a convergence rate for a time-discretization scheme by simulation to an RIBSDE. We also...

Dynamic programming and mean-variance hedging in discrete time.

Gugushvili, S. (2003)

Georgian Mathematical Journal

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

Thorsten Schmidt, Stefan Tappe (2015)

Banach Center Publications

This paper considers dynamic term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We study general forward rate curves driven by infinitely many Brownian motions and an integer-valued random measure, generalizing existing approaches in the literature. A precise characterization of absence of arbitrage in such markets is given in terms of a suitable criterion for no asymptotic free lunch (NAFL). From this, we obtain drift conditions which are equivalent...