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July 2020

Ms Kate Menzel

Honours graduate


Office: 721 |

Honours thesis

Accumulated reward in Markov reward models

In this project we consider a number of methods which can be used to numerically evaluate the moments of accumulated reward of a Markov reward model. Two existing methods given by Castella et al. [3] are first summarised, then an alternative approach is introduced, utilising path integral techniques. We find that the path integral approach may be solved in two ways, using either an ordinary differential equation solver or by way of matrix exponentials. These methods are initially given in context of an irreducible process, but later are extended to the case of a reducible process, where we find that certain methods, in particular the extremely efficient matrix exponential method, do not necessarily work in all cases we consider. The accumulated reward of a process is then given in a physical context where it is considered as a possible measure of risk of extinction for a population. We find that the measure does in fact summarise the risk of population extinction quite effectively.