Numerical Calculations of Static and Dynamic Optimal Consumption and Products

Specialeforsvar ved Ida Egede Andersen

Titel: Numerical Calculations of Static and Dynamic Optimal Consumption and Products

Abstract:  This paper deals with the choices of individuals who wish to take out life insurance. We start out in a one-life life-death model and provide a detailed mathematical description of a number of utility optimization problems that our policyholder could be facing. We solve the problem with static premium, death sum and pension payment, i.e. they are chosen at initiation and fixed thenceforth. We also solve the problem where the controls can be chosen dynamically, one case where the controls are fixed at pension time and one where they are dynamic also through retirement. We perform numerical calculations and find that all the optimal consumption rates are decreasing when the policyholders subjective discount rate is larger than the interest rate. Our results turn out to be more or less similar to results presented in an article by Kraft & Steffensen (2008), although there are some remarkable differences in our numerical findings which partly seems to be because the article do their calculations with fixed death sum. The second part of the paper describes the utility optimization problem of a married couple where the husband pays premium and both receive pension payments resulting in 5 controls. We find static controls in a ’standard’ way and in a more special way and find that the results of the first version can be reduced to the controls from the one-life model when eliminating the two-life aspects. We also find dynamic optimal controls for the couple, which we find confirmed by an article by Bruhn & Steffensen (2010). 

Vejleder:  Mogens Steffensen
Censor:    Jesper Olesen, Danica Pension