Insurance drawdown-type contracts for a phase-type risk process perturbed by Brownian motion

• Authors: Zbigniew Palmowski , Joanna Tumilewicz
• Languages of publication: PL EN

Abstracts

EN

In this paper we consider the insurance polices based on drawdown and drawup events where an underlying asset is derived by a classical risk process with phasetype claim sizes perturbed by Brownian motion. The drawdown/drawup process we define as a difference between the historical maximum/minimum and current asset value. We consider four contracts presented in [Palmowski, Tumilewicz 2016]. The first one is an insurance contract where the protection buyer is paying a constant premium with intensity p until the drawdown of fixed size occurs. In return he/she receives a certain insured amount at the drawdown epoch. The second insurance contract may expire early if a certain fixed drawup event occurs prior to a fixed drawdown. The last two contracts are extensions of the previous ones by an additional cancellable feature which allows an investor to terminate the contract earlier. We focus here on an extensive numerical analysis when claim sizes are phase-type.

Keywords

EN

insurance contract; fair valuation; drawdown; Lévy process; drawup; optimal stopping; Brownian motion

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Śląski Przegląd Statystyczny
• Year: 2017
• Issue: 15 (21)
• Pages: 201-226

Contributors

author

Zbigniew Palmowski

author

Joanna Tumilewicz