In 1999 Tomasz Bielecki and Stanley Pliska proposed an alternative to the Merton model based on a risk-sensitive control criterion (Bielecki and Pliska, 1999). Their risk-sensitive asset management model has three appealing features: the optimisation criterion is intuitive, it is consistent with financial and economic theory, and it models explicitly the impact of exogenous factors on asset prices. Kazutaka Kuroda and Hideo Nagai (Kuroda and Nagai, 2002) soon made the connection between risk-sensitive asset management and linear regulator problems. A measure change along the lines of Section 1.4 provides the key argument. In parallel, Bielecki, Pliska and their coauthors extended risk-sensitive asset management in a series of articles published between 1999 and 2005 (Bielecki and Pliska, 1999; Bielecki et al., 1999; Bielecki and Pliska, 2000; Bielecki et al., 2000, 2001, 2002; Bielecki and Pliska, 2003, 2004; Bielecki et al., 2004, 2005)The objective of this chapter is to present the risk-sensitive asset management model in a 'diffusion' setting similar to that of Chapter 1 and to lay the foundations for the exploration of benchmarks, asset and liability management and jump-diffusion models in later chapters.
