This paper develops a general theory of irreversible investment of a single firm that chooses a dynamic capacity expansion plan in an uncertain environment. The model is set up free of any distributional or any parametric assumptions and hence encompasses all the existing models. As the first...

We study the skewness premium (SK) introduced by Bates (1991) in a general context using Lévy Processes. Under a symmetry condition Fajardo and Mordecki (2006) have obtained that SK is given by the Bate's x% rule. In this paper, we study SK under the absence of that symmetry condition. More...

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by...

In this paper we compute equivalent martingale measures when the asset price return is modeled by a Lévy process. We follow the approach introduced by Gerber and Shiu (1994).

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 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...