Optimal portfolio model under compound jump processes

Abstract

PurposeThe purpose of this paper is to research the optimal portfolio proportion for the optimal investment model and the optimal consumption investment strategies for the optimal consumption investment model under compound‐jump processes.Design/methodology/approachTraditionally, the price of risky security or asset is often modeled as geometric Brownian motion. However, the analysis of stock price evolution reveals sudden and rare breaks logically accounted for by exogenous events on information. It is natural to model such behavior by means of a point process, or, more simply, by a Poisson process, which has jumps of constant size occurring at rare and unpredictable intervals. Assume that the price of risky security stock is modeled by a compound‐jump process, the renew process theory is chosen to solve the optimal investment model, the HJB equation is chosen for the optimal consumption investment model.FindingsDerive the analytical optimal portfolio proportion for the reduction model of optimal investment. The optimal consumption investment strategies are given by some equations for the optimal consumption investment model.Research limitations/implicationsAccessibility and availability of data are the main limitations which model will be applied.Practical implicationsThe results obtained in this paper could be used as a guide to actual portfolio management.Originality/valueThe new approach for the optimal portfolio model under compound‐jump processes. The paper is aimed at actual portfolio managers.