Mathematical and Statistical Methods for Actuarial Sciences and Finance

A financial analysis of surplus dynamics for

deferred life schemes∗

Rosa Cocozza, Emilia Di Lorenzo, Albina Orlando, and Marilena Sibillo

Abstract.The paper investigates the financial dynamics of the surplus evolution in the case

of deferred life schemes, in order to evaluate both the distributable earnings and the expected

worst occurence for the portfolio surplus. The evaluation is based on a compact formulation

of the insurance surplus defined as the difference between accrued assets and present value of

relevant liabilities. Thedynamic analysis is performed by means of Monte Carlo simulations

in order to provide a year-by-year valuation. The analysis is applied to a deferred life scheme

exemplar, considering that the selected contract constitutes the basis for many life insurance

policies and pension plans. The evaluation is put into an asset and liability management deci-

sion-making context, where the relationships between profits and risks are compared in order

to evaluate the main features of the whole portfolio.

Key words:financial risk, solvency, life insurance

1 Introduction

The paper investigates the financial dynamics of surplus analysis with the final aim

of performing a breakdown of the distributable earnings. The question, put into an

asset and liability management context, is aimed at evaluating and constructing a sort

of budget of the distributable earnings, given the current information. To this aim, a

general reconstruction of the whole surplus is performed by means of an analytical

breakdown already fully developed elsewhere [1], and whose main characteristic is

the computation of a result of the portfolio, that actuaries would qualify as surplus,

accountants as income and economists as profit.

The analysis is developed with the aim of evaluating what share of each year’s

earnings can be distributed without compromising future results. This share is only a

sort of minimum level of distributed earnings which can serve as a basis for business

decisions and that can be easily updated year-by-year as market conditions modify.

Then the formal model is applied to a life annuity cohort in a stochastic context in

∗Although the paper is the result of a joint study, Sections 1, 2 and 4 are by R. Cocozza,

whilst Section 3 is by E. Di Lorenzo, A. Orlando and M. Sibillo.

M. Corazza et al. (eds.), Mathematical and Statistical Methodsfor Actuarial Sciencesand Finance
© Springer-Verlag Italia 2010