Unit-linked life insurance policies: Optimal hedging in partially observable market models

Abstract

Abstract. In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor that also influences the mortality rate of the policyholder. To allow for mutual dependence between the financial and the insurance markets, we use the progressive enlargement of filtration approach.We characterize the optimal hedging strategy in terms of the integrand in the Galtchouk-Kunita-Watanabe decomposition of the insurance claim with respect to the minimal martingale measure and the available information flow. We provide an explicit formula by means of predictable projection of the corresponding hedging strategy under full information with respect to the natural filtration of the risky asset price and the minimal martingale measure. Finally, we discuss applications in a Markovian setting via filtering.

Mortality/Longevity Risk-Minimization with or without Securitization

“…Concerning the literature about risk-minimization with or without mortality securitization, we cite [7,8,17,[26][27][28][29][30][31][32][33] and the references therein to cite a few. In [8,32,33], the authors assume independence between the financial market and the insurance model, a fact that was criticized in [34].…”

“…To our knowledge, all the literature considers the Brownian setting for the financial market except for [17]. In [30,31], the authors accounted for the mutual dependence between the financial and the insurance markets (and also for partial information on the mortality intensity of the policy holder) but assumed a particular hazard rate process for the mortality and worked in a Brownian setting. The application to the semimartingale case via the weaker concept of local risk minimization in [30] is by the continuity of the processes essentially reduced to finding the Galtchouk-Kunita-Watanabe decomposition under the minimal martingale measure.…”

CEO Overconfidence and Shadow-Banking Life Insurer Performance Under Government Purchases of Distressed Assets

“…3 The insurance industry is one of the largest institutional investors in Europe (Insurance Europe and Oliver Wyman 2013). 4 For example, see Briys and de Varenne (1994); Grosen and Jørgensen (2002); Chen and Suchanecki (2007); and Ceci et al (2017). The issue of life insurance settlement presented by Hong and Seog (2018) is an exception.…”

Hedging strategy for unit-linked life insurance contracts with self-exciting jump clustering

“…To get over it, they obtain the real locally risk-minimizing hedging strategies for unit-linked life contracts. For other relevant works, interested readers may refer to [29], [21], [6] and [7].…”

“…In this subsection, we will introduce the combined financial-insurance model. Motivated by [27], [32], [37], [7], we assume in our work that the insurance market is independent of the financial market and that the hazard rate is a deterministic function. Under this assumption, future lifetime of an individual does not depend on the dynamics of financial market.…”