Explicit Föllmer-Schweizer decomposition of life insurance liabilities through Malliavin calculus
(2014) SCOR papers — Vol. 30, n° 1, p. 1-28 (2014)
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- Abstract
- (en) This paper addresses the problem of finding hedging strategies in an incomplete market. We study the Föllmer-Schweizer decomposition of a life insurer’s liabilities (involving stochastic mortality and financial profit sharing), splitting them into a component that can be hedged on the financial market and a component that cannot. Using Malliavin calculus tools, we obtain an explicit formula for each part, and therefore a complete probabilistic description of both components of the liabilities (the hedgeable and non-hedgeable). In addition to the optimal risk-minimizing “hedging" strategy, it allows to compute various business-related quantities, such as e.g. the risk margin (as defined in Solvency II) associated with the balance sheet. Two different models for the financial asset available for investment are considered.
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de Valeriola, S. (2014). Explicit Föllmer-Schweizer decomposition of life insurance liabilities through Malliavin calculus. SCOR papers, 30(1), 1-28. https://hdl.handle.net/2078.5/195659 (Original work published 2014)