Roczniki Kolegium Analiz Ekonomicznych

Issue 51/2018

The CEA states that the primary version is the paper one.

Zbigniew Palmowski, Joanna Tumilewicz

Zabezpieczenie przed spadkiem wartości aktywów w modelu typu Lévy’ego z fazowymi skokami i dowolną funkcją wynagrodzenia

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Drawdown insurance contracts for the Lévy-type model with the phase-type jump distribution and general reward function

Abstract
In this paper, we consider an insurance contract which insure against a fall of some pre-specified level below an asset’s maximal value. This situation may cause huge losses to investors and it gives a reason to create an insurance against such a situation. We model a risky asset by the geometric Browanian motion with jumps having the phase-type distribution. We define the drawdown proces as a difference between the supremum of underlying process and its current value. For this model, we construct insturance against a huge drawdown. In this contract, an insurance company commits to pay reward at a drawdown epoch. In return, an investor pays continuously a consant premium up to the drawdown moment. This work is based on the paper of Palmowski and Tumilewicz18, in which the authors presented a mathematical model for some insurance contracts against the drawdown for spectrally negative Lévy processes. Here, we focus on numerical analysis of one of such contracts when jumps are of the phase-type.

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Table of contents of issue 51

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