Pricing variable annuity with surrender guarantee
type: Item
instance of: scholarly article
title: Pricing variable annuity with surrender guarantee
zbMATH Open document ID: 1471.91463
author: Junkee Jeon
author: Minsuk Kwak
published in: Journal of Computational and Applied Mathematics
publication date: 2021-04-23T00:00:00Z
review text: A variable annuity with guaranteed sum \(G_t = G e^{g t}\) at time \(t\) is invested in a fund modelled as a Black-Scholes market \[d S_t = r S_t \; d t + \sigma S_t \;d W_t\;,\] where all processes are considered under the pricing measure. A fixed part of the wealth is taken for the management of the fund, so that the fund follows \[d F_t = (r-c) F_t \; d t + \sigma F_t \;d W_t\;.\] At maturity, the policy holder will get \(\max\{F_T,G_T\}\). Moreover, the policy holder has the possibility to surrender. Three possible surrender values are considered: (1) \(e^{-\kappa(T-t)} \max\{F_t, G_t\}\), (2) \(e^{-\kappa(T-t)} F_t\), (3) \(e^{-\kappa(T-t)} G_t\). The corresponding optimal stopping theorems are formulated, the variational inequalities are given and the continuation and surrender regions are defined. The main theorem shows that the value function can be split into an European part and an early surrender premium part. The European part is given explicitly, the early surrender part in terms of the boundaries between the continuation and surrender regions. Several figures illustrate the regions.
reviewed by: Hanspeter Schmidli
Mathematics Subject Classification ID: 91G05
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 7337484
zbMATH Keywords: variable annuity
zbMATH Keywords: surrender guarantee
zbMATH Keywords: optimal surrender
zbMATH Keywords: double surrender region
MaRDI profile type: Publication
full work available at URL: j.cam.2021.113508
OpenAlex ID: W3133713260
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DOI: 10.1016/J.CAM.2021.113508
description: scientific article; zbMATH DE number 7337484