Continuous affine processes: transformations, Markov chains and life insurance. (English) Zbl 1414.91167

Buchardt, Kristian

Adv. Appl. Probab. 48, No. 2, 423-442 (2016).

Summary: Affine processes possess the property that expectations of exponential affine transformations are given by a set of Riccati differential equations, which is the main feature of this popular class of processes. In this paper we generalise these results for expectations of more general transformations. This is of interest in, e.g. doubly stochastic Markov models, in particular in life insurance. When using affine processes for modelling the transition rates and interest rate, the results presented allow for easy calculation of transition probabilities and expected present values.

MSC:

91B30	Risk theory, insurance (MSC2010)
91G40	Credit risk
60J20	Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)

Keywords:

doubly stochastic process; multi-state life insurance models; credit risk; stochastic mortality; stochastic interest