# Modeli tržišnog vrednovanja u životnom osiguranju : završni rad

Petrač, Maja (2015) Modeli tržišnog vrednovanja u životnom osiguranju : završni rad. Other, Faculty of Science > Department of Mathematics.

 PDF Restricted to Repository staff only Language: Croatian Download (1MB) | Request a copy

## Abstract

This work combines traditional life insurance model with financial model of the market in a discreet time. This integration is the basics of modern life insurance mathematics that introduce a new method of asset valuation - market valuation. New accounting standards and solvency regulations (Solvency II) require for insurance cash flow to be valuated in a market consistent approach. Since traditional actuary principles is not enough to evaluate and to manage different types of risk, especially those of financial or actuarial type, introduction of this work adduces reasons for induction of new valuation principle. In second chapter we induce some basic terms, definitions and theorems of the theory of measure and stochastic analysis that can be useful further in the text. In chapter 3, we bring from memory classic actuarial mathematics of life insurance. We describe basic life insurance contracts using interest rates and mortality. Formulas for (present) value of payments that depend on survival or death of a person should be used for premium calculations. Basics of modern actuarial mathematics is financial mathematics, so in chapter 4 we give a short review on basic characteristics of financial market model. Unlike traditional actuarial mathematics, expectations must be calculated in regard to a measure neutral to risk, and not to a natural measure. Market consistent valuation of modern insurance products and also total portfolio of insurance company require integrated approach that combines techniques of financial an actuarial mathematics. This is the exact issue in chapter 5. Construction of this new integrated model leads to incomplete market with lots of different martingale measures. We will show that, with certain assumptions, it is still possible to find that unique nonarbitrage price. However, integrated contingent claims that depend on both financial and insurance risk are not generally attainable, so we would need other valuation and hedging methods. This work ends with an example with real Croatian market data, so it shows influence of market valuation on specific example (several life insurance policies).

Item Type: Thesis (Other) Huzak, Miljenko 2015 73 NATURAL SCIENCES > Mathematics Završni rad na poslijediplomskom specijalističkom studiju aktuarske matematike Faculty of Science > Department of Mathematics Iva Prah 11 Jan 2016 13:09 11 Jan 2016 13:09 http://digre.pmf.unizg.hr/id/eprint/4391

 View Item

Nema podataka za dohvacanje citata