Publisher Correction: $${\texttt{openIRM}}$$: publicly accessible internal risk model of an artificial life insurer for analyzing and benchmarking actuarial methods in the solvency II setting

Abstract

Unfortunately, many of the author corrections were missed out in the original publication. The corrected information's are given below. The following issues in the article have been fully corrected: Document outline: OpenIRM now renders correctly in the document outline of PDF viewers, and the titles for Sect. 6.7 and the main document are displayed correctly. Table 1 formatting: The brace for =Vkon the right side of Table 1 is now positioned correctly. Figure sizing (Figs. 4 & 5): Fig. 4 and Fig. 5 have been correctly scaled down to their intended smaller size, no longer spanning the entire page width. This resolves the previous pixelation and oversized text issues. Figure sizing (Fig. 6): Fig. 6 has been restored to its intended full-page width double-figure size. Figure sizing and orientation (Figs. 7 & 9): Fig. 7 and Fig. 9 are now rendered clearly. The issue regarding their required size and potential landscape orientation has been resolved to ensure readability, while adhering to journal standards. (Figure presented.) Article structure and appendix placement: The structure has been corrected. The Appendix now appears after the References section, providing a clear and logical flow that no longer obscures the References. Conclusion visibility: The Conclusion section is now distinct and stands out correctly at the end of the main text, preceding the References. Page breaks and layout: All abysmal page breaks have been fixed. Equations and sentences are handled correctly across pages, and figures (e.g., Fig. 9) no longer interrupt text flow, ensuring that sections like the Conclusion start clearly on the appropriate page. The Appendix now begins on a new page. Appendix equation numbering: The equation numbers, particularly in the Appendix, are no longer overlapping the equations themselves. Structural and Formatting Adjustments:Table 2 (p. 14): Horizontal lines have been added before the rows "Capital market model", "Management model", and "Liability model" to improve readability.Table 6 (p. 37): The alignment of the first row has been corrected. The term “Risk factors” in column 2 is now a standalone line. The elements $X^{i1,1}$ (Column 1), "Interest rate factor 1" (Column 2), and $\log(X+0.32) \sim N(-1.167, 0.235^2)$ (Column 3) are now correctly aligned. Navigation and Hyperlinks:Footnote 1 (p. 8): An active hyperlink has been added to the footnote reference in the text.Appendices: Hyperlinks have been added to the following locations for easier navigationAppendix A: Referenced on p. 17, line 3.Appendix B: Referenced on p. 24 (line 1 and line 12 from bottom) and p. 25 (line 7).Appendix C: Referenced on p. 35, line 9. Equation Numbering and Referencing:Appendix Equations: The equation numbering in the Appendices has been synchronized with the main body. Textual references to non-existent high-digit equation numbers (e.g., eq. 124) have been corrected to match the actual Appendix numbering ($A1$, $A2$, etc.).Parentheses: Parentheses have been added to all referenced equation numbers throughout the text for consistency (e.g., p. 53). References and Typos:Ref. 2 (p. 56): “Solvency ii” has been corrected to the capitalized “Solvency II”.Ref. 41 (p. 58): Capitalization has been corrected for the title: “Das interne Modell der Feldafinger Brandkasse goes R”.Ref. 54 (p. 58): The broken hyperlink has been repaired. Document outline: OpenIRM now renders correctly in the document outline of PDF viewers, and the titles for Sect. 6.7 and the main document are displayed correctly. Table 1 formatting: The brace for =Vkon the right side of Table 1 is now positioned correctly. Figure sizing (Figs. 4 & 5): Fig. 4 and Fig. 5 have been correctly scaled down to their intended smaller size, no longer spanning the entire page width. This resolves the previous pixelation and oversized text issues. Figure sizing (Fig. 6): Fig. 6 has been restored to its intended full-page width double-figure size. Figure sizing and orientation (Figs. 7 & 9): Fig. 7 and Fig. 9 are now rendered clearly. The issue regarding their required size and potential landscape orientation has been resolved to ensure readability, while adhering to journal standards. (Figure presented.) Article structure and appendix placement: The structure has been corrected. The Appendix now appears after the References section, providing a clear and logical flow that no longer obscures the References. Conclusion visibility: The Conclusion section is now distinct and stands out correctly at the end of the main text, preceding the References. Page breaks and layout: All abysmal page breaks have been fixed. Equations and sentences are handled correctly across pages, and figures (e.g., Fig. 9) no longer interrupt text flow, ensuring that sections like the Conclusion start clearly on the appropriate page. The Appendix now begins on a new page. Appendix equation numbering: The equation numbers, particularly in the Appendix, are no longer overlapping the equations themselves. Structural and Formatting Adjustments: Table 2 (p. 14): Horizontal lines have been added before the rows “Capital market model”, “Management model”, and “Liability model” to improve readability. Table 6 (p. 37): The alignment of the first row has been corrected. The term “Risk factors” in column 2 is now a standalone line. The elements $X^{i1,1}$ (Column 1), “Interest rate factor 1” (Column 2), and $\log(X+0.32) \sim N(-1.167, 0.235^2)$ (Column 3) are now correctly aligned. Navigation and Hyperlinks: Footnote 1 (p. 8): An active hyperlink has been added to the footnote reference in the text. Appendices: Hyperlinks have been added to the following locations for easier navigation Appendix A: Referenced on p. 17, line 3. Appendix B: Referenced on p. 24 (line 1 and line 12 from bottom) and p. 25 (line 7). Appendix C: Referenced on p. 35, line 9. Equation Numbering and Referencing: Appendix Equations: The equation numbering in the Appendices has been synchronized with the main body. Textual references to non-existent high-digit equation numbers (e.g., eq. 124) have been corrected to match the actual Appendix numbering ($A1$, $A2$, etc.). Parentheses: Parentheses have been added to all referenced equation numbers throughout the text for consistency (e.g., p. 53). References and Typos: Ref. 2 (p. 56): “Solvency ii” has been corrected to the capitalized “Solvency II”. Ref. 41 (p. 58): Capitalization has been corrected for the title: “Das interne Modell der Feldafinger Brandkasse goes R”. Ref. 54 (p. 58): The broken hyperlink has been repaired. The Original article has been corrected.