Pricing formulae for derivatives in insurance using the Malliavin calculus

Caroline Hillairet () and Ying Jiao ()
Additional contact information
Caroline Hillairet: ENSAE; Université Paris Saclay
Ying Jiao: Université Claude Bernard - Lyon 1; Institut de Science Financière et d’Assurances

No 2017-75, Working Papers from Center for Research in Economics and Statistics

Abstract: In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at expressing the expected cash flow in terms of a building block. The former is related to the loss process which is a cumulated sum indexed by a doubly stochastic Poisson process of claims allowed to be dependent on the intensity and the jump times of the counting process. For example, in the context of Stop-Loss contracts the building block is given by the distribution function of the terminal cumulated loss, taken at the Value at Risk when computing the Expected Shortfall risk measure.

Pages: 16 pages
Date: 2017-07-13
New Economics Papers: this item is included in nep-ias and nep-rmg
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