In finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a...

In this paper we study the dynamic behavior of the term structure of Interbank interest rates and the pricing of options on interest rate sensitive securities. We posit a generalized single factor model with jumps to take into account external influences in the market. Daily data is used to test...

This paper considers the problem of pricing American options when the dynamics of the underlying are driven both by stochastic volatility following a square root process as used by Heston (1993) and by a Poisson jump process as introduced by Merton (1976). The two-factor homogeneous...

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...