A note on optimal investment-consumption-insurance in a Lévy market

摘要

In Shen and Wei (2014) an optimal investment, consumption and life insurance purchase problemfor a wage earner with Brownian information has been investigated. This paper discusses the sameproblem but extend their results to a geometric Itô–Lévy jump process. Our modelling framework isvery general as it allows random parameters which are unbounded and involves some jumps. It alsocovers parameters which are both Markovian and non-Markovian functionals. Unlike in Shen and Wei(2014) who considered a diffusion framework, ours solves the problem using a novel approach, whichcombines the Hamilton–Jacobi–Bellman (HJB) and a backward stochastic differential equation (BSDE) ina Lévy market setup. We illustrate our results by two examples.