Robert Merton opened a new chapter in finance with his two papers (Merton, 1969; Merton, 1971), reprinted in his book (Merton, 1992), on dynamic asset allocation. Aside from taking a decisive step away from Markowitz-style single-period models, these papers made the key link with stochastic control...

In this chapter, we consider the situation of an investor who manages a portfolio of assets partly funded by an external liability. This is the typical case for banks, insurance companies and hedge funds. Asset and liabilitymanagement (ALM) problems have generated a substantial literature and a...

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 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...