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...

In the preceding chapter we showed that in a model with Gaussian diffusion factors the asset allocation problem reduces, via the change of measure technique, to a controlled diffusion problem in the factor process, even though there are jumps in the asset price model. The problem can be handled...

An important feature of the diffusion-based models presented in Part I is that they can be solved analytically, and as such do not require additional work to get the optimal investment strategy and the value function (aside from solving a Riccati equation and a linear ODE)…

The following sections are included:IntroductionFinancial Market, Investment Portfolio and BenchmarkDynamic Programming and the Value FunctionExistence of a Classical (C1,2) Solution Under Affine Drift AssumptionsExistence of a Classical (C1,2) Solution Under Standard Control AssumptionsFund...

We consider a financial market with liquidity cost as in Cetin, Jarrow and Protter [3] where the supply function S"(s; ) depends on a parameter " 0 with S0(s; ) = s corresponding to the perfect liquid situation. Using the PDE characterization of Cetin, Soner and Touzi [6] of the super-hedging...