Continuous-time safety-first portfolio selection with jump-diffusion processes

Abstract

This article is concerned with continuous-time portfolio selection based on a safety-first criterion under discontinuous price processes (jump-diffusion processes). The solution of the corresponding Hamilton–Jacobi–Bellman equation of the problem is demonstrated. The analytical solutions are presented when there does not exist any riskless asset. Moreover, the problem is also discussed while there exists one riskless asset.

Keywords:

• modern portfolio
• safety-first criterion
• continuous-time portfolio model
• Poisson process
• HJB equation