Pricing formulae for derivatives in insurance using Malliavin calculus

• Main Authors: Caroline Hillairet, Ying Jiao, Anthony Réveillac
• Format: Article
• Language: English
• Published: SpringerOpen 2018-06-01
• Series: Probability, Uncertainty and Quantitative Risk
• Subjects: Cox processes; Pricing formulae; Insurance derivatives; Malliavin calculus
• Online Access: http://link.springer.com/article/10.1186/s41546-018-0028-9

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 Malliavin calculus. Similar to the celebrated Black–Scholes formula, we aim to express 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.