Izbrane teme sodobne fizike in matematike
Teorija optimalnega časa ustavljanja nam pomaga odgovoriti na vprašanje, v katerem trenutku je pričakovana korist zaustavitve slučajnega procesa maksimalna. Uporablja se na številnih področjih, v članku pa se osredotočimo na uporabo na zavarovalniških produktih z garancijo. Pri ponudbi takšnih produktov so zavarovalnice izpostavljene tveganju, pred katerim se morajo ustrezno zaščititi. Na začetku članka v splošnem predstavimo matematično podlago teorije, definiramo pojem Snellove ovojnice in predstavimo njeno uporabo. Sledi aplikacija teorije, kjer predstavimo dve varovalni strategiji zavarovalnice. Ena od teorij temelji na iskanju najbolj ustreznega časa za nakup prodajne opcije, ki ob izteku pogodbe zagotavlja zadostna sredstva za izplačilo zavarovanca. Strategiji primerjamo glede na porazdelitev končne izgube, rezultati pa so podprti tudi s kratko simulacijo.
The theory of optimal stopping time helps us answer the question, at what point in time the expected benefit of stopping a random process is maximized. Although the theory is applicable in many fields, this article will focus on its application in insurance products with guarantees. The risk arising from such products must be hedged by suitable investments.At the beginning of the article we give a general introduction to the mathematical basis of the theory, define the concept of Snell envelope and present its applicability.This is followed by a practical use of the theory, where we present two hedging strategies of an insurance company. One of the theories is based on finding the most appropriate time to buy a put option, which, at the expiry of the contract,provides sufficient funds to pay out the guaranteed amount. The two strategies are compared with respect to the insurer’s ultimate loss distribution, and the results are supported by a short simulation.