Infinite Horizon Problems

Mark H. A. Davis and Sebastien Lleo

Chapter 6 in Risk-Sensitive Investment Management, 2014, pp 109-128 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The problem we have considered so far relates to the finite horizon criterion $$J_{RS}^\theta (t;\,x,\,h)\,: = \, - {1 \over \theta }\ln {\Bbb E}{e^{ - \theta F(t;\,x,\,h)}}$$. There is also a rich literature on risk-sensitive control problems set over an infinite horizon, including Bielecki and Pliska (1999); Fleming and Sheu (2000, 2002); Kuroda and Nagai (2002). The typical criterion in this case is to maximise the risk-sensitive expected log return per unit of time, that is $$J_{RS}^\theta (\infty ;{\mkern 1mu} \,x,{\mkern 1mu} \,h){\mkern 1mu} \,: = {\mkern 1mu} \,{\mathop {\lim\, \inf}\limits_{t \to \infty} - \frac{1}{\theta }{t^{ - 1}}\ln {\Bbb E}{e^{ - \theta \ln \,\,V(t)}}. \kern+60pt (6.1)$$…

Keywords: Stochastic Control; Risk Sensitive Control; Dynamic Investment Management; Benchmarked Asset Management; Asset and Liability Management; Jump Diffusion Processes; Lévy Processes; Hamilton–Jacobi–Bellman Equations; Classical Solutions; Viscosity Solutions; Kelly Criterion (search for similar items in EconPapers)
Date: 2014
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