In this paper we are concerned with analysing optimal wealth allocation techniques within a defaultable financial market similar to Bielecki and Jang (2007). We study a portfolio optimization problem combining a continuous-time jump market and a defaultable security; and present numerical solutions through the conversion into a Markov decision process and characterization of its value function as a unique fixed point to a contracting operator. In this paper we analyse allocation strategies under several families of utility functions, and highlight significant portfolio selection differences with previously reported results.
"Markov decision process algorithms for wealth allocation problems with defaultable bonds." Adv. in Appl. Probab. 48 (2) 392 - 405, June 2016.