Stochastic asset liability modelling in life insurance

Abstract

The aim of this dissertation is to create an Asset Liability Model for a life insurance company using Stochastic Differential Equations. The assets will be modelled using continuous Stochastic Differential Equations, and the liabilities, in our case, the claims, will be modelled using the Compound Poisson Process. Special attention will be given to the development of the stochastic calculus of Stochastic Differential Equations with jumps. Then, the dissertation will conclude by running simulations on our Asset Liability Model. These will be performed using the Euler Discretization Scheme, and the parameters estimated using the Method of Maximum Likelihood.