Fair Dynamic Valuation of Insurance Liabilities via Convex Hedging

Fair dynamic valuation of insurance liabilities: a loss averse convex hedging approach

“…We next revisit the fair dynamic valuations introduced by and Chen et al (2019). In the multi-period setting, a t−valuation ρ t assigns to each T −claim a G t −measurable random variable ρ t [S] that represents the t−value of the T −claim S, given the available information at time t. A dynamic valuation is a sequence of t−valuations 2 .…”

“…Dhaene et al (2017) and proposed fair (dynamic) valuation techniques for valuating insurance liabilities in both single-period and multi-period settings and showed that fair valuation is equivalent to a hedge-based valuation approach. Moreover, Dhaene et al (2017) and Chen et al (2019) showed that the class of fair (dynamic) valuation is equivalent to convex hedge-based, or CHB, (dynamic) valuations. Specifically, the fair valuation of insurance liabilities follows a two-stage process.…”

“…The fair value is then the sum of the market value of the hedge and the risk margin value of the residual claim (Figure 1). In this study, we extend the work of and Chen et al (2019) by investigating the fair valuation of insurance liabilities using loss averse convex (LAC) hedging, a particular class of convex hedging, in a multi-period setting. The underlying optimization convex function of LAC hedging 'punishes' loss outcomes more than gain outcomes.…”

“…Our work is related to several streams of the literature. The first stream is related to works on market-consistent and fair valuations of insurance liabilities such as Dhaene et al (2017), , Chen et al (2019), Salzmann and Wüthrich (2010), Moehr (2011), Tsanakas et al (2013), Wüthrich et al (2013), and Pelsser and Stadje (2014). Another related field is the study of the actuarial valuation principle, including the studies by Kaas et al (2008) and Norberg (2014).…”

“…In Section 2, we define the general framework of the financial-actuarial world. In Section 3, we revisit the dynamic fair and CHB valuation framework of Chen et al (2019) and introduce LAC hedge-based (LACHB) and dynamic hedging and valuation. In Section 4, we propose the LAMV dynamic hedge and valuation as well as provide complete characterizations.…”