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Papers by Frederic Sart
Journal of Applied Analysis, 2023
In this paper we prove the Belitskii–Lyubich conjecture for triangular and gradient mappings. The... more In this paper we prove the Belitskii–Lyubich conjecture for triangular and gradient mappings. These results resemble those obtained for the discrete Markus–Yamabe conjecture. However, the proofs are quite different, which sheds new light on the subject. We complete the picture by showing that the general versions of the two conjectures can be turned into theorems at little cost, simply by relaxing their spectral condition.
Bulletin Français d'Actuariat, 2016
The fair replication method is a method designed to value liabilities with an endogenous profit s... more The fair replication method is a method designed to value liabilities with an endogenous profit sharing mechanism, i.e. based on the book yield of the backing assets. The basic idea is to construct a hypothetical portfolio, the fair replicating portfolio (FRP), whose cash flows are scenario-invariant. The method is a computationally efficient alternative to traditional stochastic modeling. It may be particularly useful in applications where extensive calculations of best estimate of liabilities are required.
Journal of Applied Analysis, 2010
In this paper we develop a new method for valuing universal life policies via a zero-coupon bond ... more In this paper we develop a new method for valuing universal life policies via a zero-coupon bond replicating portfolio. The method combines the idea of replicating portfolio with that of a fixed point. In addition, we accompany the proposed method with an equation relating account value, reserve and present value of future profits.
Logique et Analyse, 2009
In this paper I revisit the foundations of deontic logic. This results in a truth-table way of lo... more In this paper I revisit the foundations of deontic logic. This results in a truth-table way of looking at the deontic modality. Going back to Frege, I de ne a semantics for deontic logic on the basis of four primitive terms (the) True, (the) False, (the) Permitted, (the) Forbidden without introducing an accessibility relation.
Journal of Applied Analysis, 2007
In this paper, we give a fixed point theorem for triangular mappings whose derivatives are bounded.
Dissertation, 2000
Starting from Frege's Logische Untersuchungen, we lay down that logic is the study of proposition... more Starting from Frege's Logische Untersuchungen, we lay down that logic is the study of propositions, that is the study of what is either true or false. In order to analyze propositions, we have used a method based on two successive steps:
1. To formalize, that is to reduce logic to a formal logic. In other words, the question is, within a finite propositional frame:
• 1.1. To define a concept of configuration and, based on this, a concept of truth-function (on the - finite – space of configurations).
• 1.2. To link the second concept to that of proposition by assuming that each truth-function expresses a proposition.
2. To symbolize, that is to transform this formal logic into symbolic logic. In other words, the question is then:
• 2.1. To define a concept of formula.
• 2.2. To link this concept to that of truth-function by defining a semantics by recurrence, viz. a function such that a truth-function corresponds to any formula.
A logic grounded on this method will thus comprehend a double representation: the first will be formal; the second, symbolic.
We defend the thesis that the deontic question can be resolved according to this method. Our alethico-deontic logic is a proof of this thesis. It is divided into two sections: the case of an Authority is first expounded, and then that of a finite set of Authority(ies). It is prefigured by our alethic logic, that draws to a certain extent on Wittgenstein's Tractatus logico-philosophicus.
Talks by Frederic Sart
Thoughts by Frederic Sart
Journal of Applied Analysis, 2023
In this paper we prove the Belitskii–Lyubich conjecture for triangular and gradient mappings. The... more In this paper we prove the Belitskii–Lyubich conjecture for triangular and gradient mappings. These results resemble those obtained for the discrete Markus–Yamabe conjecture. However, the proofs are quite different, which sheds new light on the subject. We complete the picture by showing that the general versions of the two conjectures can be turned into theorems at little cost, simply by relaxing their spectral condition.
Bulletin Français d'Actuariat, 2016
The fair replication method is a method designed to value liabilities with an endogenous profit s... more The fair replication method is a method designed to value liabilities with an endogenous profit sharing mechanism, i.e. based on the book yield of the backing assets. The basic idea is to construct a hypothetical portfolio, the fair replicating portfolio (FRP), whose cash flows are scenario-invariant. The method is a computationally efficient alternative to traditional stochastic modeling. It may be particularly useful in applications where extensive calculations of best estimate of liabilities are required.
Journal of Applied Analysis, 2010
In this paper we develop a new method for valuing universal life policies via a zero-coupon bond ... more In this paper we develop a new method for valuing universal life policies via a zero-coupon bond replicating portfolio. The method combines the idea of replicating portfolio with that of a fixed point. In addition, we accompany the proposed method with an equation relating account value, reserve and present value of future profits.
Logique et Analyse, 2009
In this paper I revisit the foundations of deontic logic. This results in a truth-table way of lo... more In this paper I revisit the foundations of deontic logic. This results in a truth-table way of looking at the deontic modality. Going back to Frege, I de ne a semantics for deontic logic on the basis of four primitive terms (the) True, (the) False, (the) Permitted, (the) Forbidden without introducing an accessibility relation.
Journal of Applied Analysis, 2007
In this paper, we give a fixed point theorem for triangular mappings whose derivatives are bounded.
Dissertation, 2000
Starting from Frege's Logische Untersuchungen, we lay down that logic is the study of proposition... more Starting from Frege's Logische Untersuchungen, we lay down that logic is the study of propositions, that is the study of what is either true or false. In order to analyze propositions, we have used a method based on two successive steps:
1. To formalize, that is to reduce logic to a formal logic. In other words, the question is, within a finite propositional frame:
• 1.1. To define a concept of configuration and, based on this, a concept of truth-function (on the - finite – space of configurations).
• 1.2. To link the second concept to that of proposition by assuming that each truth-function expresses a proposition.
2. To symbolize, that is to transform this formal logic into symbolic logic. In other words, the question is then:
• 2.1. To define a concept of formula.
• 2.2. To link this concept to that of truth-function by defining a semantics by recurrence, viz. a function such that a truth-function corresponds to any formula.
A logic grounded on this method will thus comprehend a double representation: the first will be formal; the second, symbolic.
We defend the thesis that the deontic question can be resolved according to this method. Our alethico-deontic logic is a proof of this thesis. It is divided into two sections: the case of an Authority is first expounded, and then that of a finite set of Authority(ies). It is prefigured by our alethic logic, that draws to a certain extent on Wittgenstein's Tractatus logico-philosophicus.