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...

The objective of this chapter is to illustrate how some of the models developed in the first part of the book can be useful to address practical investment management questions. We consider four short cases. The first one explores the interest of including a factor X(t) compared to the...

The Oxford English Dictionary defines a benchmark, or more precisely a ‘bench-mark’, as ‘a surveyor's mark cut in some durable material, as a rock, wall, gate-pillar, face of a building, etc., to indicate the starting, closing, or any suitable intermediate point in a line of levels for the...

The following sections are included:IntroductionFinancial Market, Investment Portfolio and LiabilityFormulation of the Asset and Liability Management ProblemDynamic Programming and the Value FunctionSolving the ALM Problem Under Affine Drift AssumptionsSolving the ALM Problem Under Standard...

In the diffusions setting introduced in Part I, investment management models have a significant benefit: they generate an investment strategy in closed form. This closed form strategy can be transformed, via a fund separation theorem or a fractional Kelly strategy, into a practical recipe for...

In the investment models we have considered so far, the fund manager could set the investment policy freely, as long as the allocation to each of the assets remained finite. In practice the situation is different. Fund managers are subject to investment constraints set by regulatory bodies,...

In Part I of this book, asset prices and factor processes were represented by diffusion processes, driven by correlated Brownian motions. In Part II we extend the theory — using as far as possible the same general approach — to jump-diffusion processes, where the driving Brownian motions are...

Portfolio optimisation models, whether static or dynamic, are inscribed within a much wider portfolio management framework. The current industry standard is the three-step portfolio management process proposed by Maginn et al. (2007). This process finds its roots in Markowitz' famous ‘two...

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...

We mentioned in Chapter 2 that the factor process X(t) in our models has two possible interpretations. Its components Xi(t) may represent observable data series, either financial data such as stock indices, bond yield spreads etc., or macroeconomic data such as GDP growth, employment data or...