Academic on rcor

Exposing Sleeping Beauty: Triggered or Induced?

Mon, 28 Sep 2026 00:00:00 +0000

Beauty wakes up on Monday morning.also on Tuesday, if Tails.with no memory, every time anew.when asked about her credence in Heads.

We have discussed before the distinction between a process being triggered and an outcome being induced. The distinction may look semantic at first sight, but it becomes probabilistically important whenever the observation available to an agent is produced by a mechanism that selects, filters, or repeats possible states.

The 100 Prisoners Problem: Induced vs. Triggered Processes in Risk Management

Sat, 25 Apr 2026 00:00:00 +0000

In a previous post, we established a vital distinction: the difference between an induced event (arising from human intervention) and a triggered one (the release of pre-existing tension in a system).

A rigorous distinction between triggered and induced processes can be formalized using the 100 prisoners problem, as discussed in both the algorithmic literature Gál and Miltersen (2007)) and expository mathematical sources Pahor (2024), or even as a riddle video.

While there are many variations and related paradoxes, this formulation is particularly revealing from a structural perspective: it produces one of the largest known gaps between a naive triggered interpretation and a structurally correct induced one, leading to dramatically different outcomes.

From admissible probabilities to equivalent martingale measures

Tue, 20 Jan 2026 00:00:00 +0000

The article Holtan (2007) integrates option valuation theory with practical pricing in non-life insurance, analyzing both no-arbitrage and martingale approaches, as well as complete and incomplete market settings from a supply-and-demand perspective.

According to the precise definition given by Harrison and Pliska (1983), a financial market is complete if and only if there exists a unique equivalent martingale measure associated with the underlying stochastic process. In this context, any contingent claim can be fully hedged if and only if the martingale measure is unique Shreve (2004), reinforcing the link between market completeness and full risk coverage.

Formal Foundations (ZFC) and Epistemic Desiderata

Thu, 25 Dec 2025 00:00:00 +0000

The ZFC system (Zermelo–Fraenkel + Axiom of Choice) is the standard foundation of modern mathematics. This article concisely presents the axioms so they can be cited later, including in actuarial contexts where event spaces, measurable functions, portfolio aggregations, and recursive transformations rely directly on these foundations.

In the literature, there are two numbering conventions:

the compact form (ZF with 8 axioms, Choice as the 9th), also used on Wikipedia;
the extended form used in modern treatises (Kunen, Jech), where Regularity appears explicitly and the Separation and Replacement schemes are listed separately.

Here we use the second convention, resulting in ten labels ZFC1 – ZFC10.

Choosing the Right Path

Sat, 01 Nov 2025 00:00:00 +0000

We will address the unique matching problem and its variants — a classic metaphor for decision, information, and bounded rationality.

Although similar concerns appear as early as the 18th century, when Abraham de Moivre discusses probability problems in The Doctrine of Chances De Moivre (1718), he does not directly formulate the matching problem in this manner. In the algorithmic literature, similar structural operations appear later: Quicksort Hoare (1961) solves, through a divide et impera strategy, subproblems that resonate with the logic of pair matching; subsequently, the same idea is used (and adapted) to address the problem known in the literature as nuts and bolts Alon et al. (1994).