Solving a Hamilton–Jacobi–Bellman equation with constraints

Abstract

Optimal investment strategies for an insurer with state-dependent constraints are computed via a recursive finite difference solution to the corresponding discretized Hamilton–Jacobi–Belman equation. Convergence is derived from viscosity solution arguments. For this, a comparison result is given which is similar to the result given by Azcue and Muler [Ann. Appl. Probab. 20 (2010), pp. 1253–1302].

Keywords:

• optimal investment
• maximal survival probability
• constraints
• viscosity solutions

Keywords:

• Primary: 93E20, 91B30
• Secondary: 49L25, 65M06

Notes

This article was originally published with errors. This version has been corrected. Please see Letter (http://dx.doi.org/10.1080/17442508.2015.1089244).

^1. In the sense of [9] (p. 210, Def. 4.2).