Jump-Diffusion Risk-Sensitive Asset Management II: Jump-Diffusion Factor Model

Abstract

In this article we extend our earlier work on the jump-diffusion risk-sensitive asset management problem in a factor model [SIAM J. Financial Math., 2 (2011), pp. 22--54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the Hamilton--Jacobi--Bellman (HJB) equation is a partial integro-differential equation (PIDE). We are able to show that finding a viscosity solution to this PIDE is equivalent to finding a viscosity solution to a related PDE, for which classical results give uniqueness. With this in hand, a policy improvement argument and classical results on parabolic PDEs show that the HJB PIDE admits a unique smooth solution. The optimal investment strategy is given by the feedback control that minimizes the Hamiltonian function appearing in the HJB PIDE.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 34 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.