My research focuses on three distinct areas: modal logic, actuarial science and fixed point theory.
Extension of Wittgenstein's analysis of propositions to deontic logic. Basically, I extend what Wittgenstein calls the description of the world (see §4.26 of the Tractatus logico-philosophicus) by adding to it a deontic component, defined in the most natural way.
Extension to participating contracts of the exact cash flow matching technique, which requires only fixed income securities. For this purpose, I assume that profit sharing as well as policyholder behavior are endogenous. These two assumptions are crucial in that they allow me to find – as in the Black-Scholes model – an investment strategy that eliminates risk and thus makes the valuation of these contracts deterministic. Mathematically, this amounts to formulating the problem in terms of a fixed point equation. Since very few iterations are needed to obtain an accurate result, this makes it an attractive alternative to stochastic modeling.
Proof of a fixed point theorem for triangular mappings.
https://independent.academia.edu/FredericSart