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A Discrete Risk-Theory Approach to Manage Equity-Linked Policies in an Incomplete Market

Francesco Della Corte (francesco.dellacorte1@unicatt.it) and Francesca Marzorati
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Francesco Della Corte: Department of Mathematics for Economic, Financial and Actuarial Sciences, Università Cattolica del Sacro Cuore, 20123 Milano, Italy
Francesca Marzorati: Department of Mathematics for Economic, Financial and Actuarial Sciences, Università Cattolica del Sacro Cuore, 20123 Milano, Italy

JRFM, 2024, vol. 17, issue 4, 1-17

Abstract: We construct a model where, at each time instance, risky securities can only take a limited number of values and the equity-linked policy sold by the insurer to policyholders pays benefits linked to these securities. Since the number of states in the model exceeds the number of securities in the (incomplete) market, the martingale measure is not unique, posing a problem in pricing insurance instruments. In this framework, we consider how a super-replicating strategy violates the assumption of absence of arbitrage, yet simultaneously allows the insurance company to fully hedge against financial risk. Since the super-replicating strategy, when considered alone, would be too costly for any rational insured person, through the definition of the safety loading, we demonstrate how the insurer can still hedge against financial risk, albeit at the expense of increasing its exposure to demographic risk. This approach does not aim to show how the pricing of the index-linked policy can actually be performed but rather highlights how risk theory-based approaches (via the definition of the profit and loss random variable) enable the management of the trade-off between financial risk and demographic risk.

Keywords: risk theory; safety loading; CRR; equity-linked policies; incomplete markets (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2024
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