Introduction

The liabilities of the preceding chapter extended over decades, and assets covering them should be followed over decades too, which requires models for equities and the interest-rate curve. Inflation is relevant too, since liabilities might depend on the future wage or price level. This chapter is on the joint and dynamic modelling of such variables. This is a cornerstone when financial risk is evaluated and makes use of linear, normal and heavy-tailed models, stochastic volatility, random walks and stationary stochastic processes. The topic is not elementary; above all it is multivariate. Economic and financial variables influence each other mutually, some of them heavily.

The central models, reviewed below and extended from the treatment in Part I, are huge classes, and here is the real difficulty: Which models to pick in specific situations and what about their parameters? Sources of information are historical data, implications of market positions and even economic and financial analyses and theory. Much of that is beyond the scope of this book, and unlike elsewhere model building through historical data is touched on only briefly. A specific model to work with will be needed in Chapter 15. The most established in actuarial science may be the Wilkie models, set up in a purely empirical way by examining historical data from the last 70 years of the twentieth century; see Wilkie (1995). A major part of it is presented in Sections 13.5 and 13.6.