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炭素オフセット投資のための多目的資本資産評価モデルの予備的探求：異なる接平面のヒューリスティックな証明

On Preliminarily Exploring Multiple-Objective Capital Asset Pricing Models for the Investments of Carbon Offset: Heuristically Proving Different Tangent Planes (原題)

Long Lin, Yue Qi

Mathematics📚 査読済 / ジャーナル2026-09-02#気候金融Origin: CN
DOI: 10.3390/math14173156
原典: https://doi.org/10.3390/math14173156

🤖 gxceed AI 要約

日本語

本論文は、炭素オフセット投資に特化した多目的ポートフォリオ選択モデル（MOPS）と多目的資本資産評価モデル（MOCAPM）を提案する。最小分散曲面の凸性や非劣性などの数学的性質を証明し、CAPMの一意な接線ではなく複数の接平面が存在することをヒューリスティックに示す。理論的な足がかりを提供する。

English

This paper proposes a multiple-objective portfolio selection model (MOPS) and explores multiple-objective capital asset pricing models (MOCAPM) for carbon offset investments. It proves mathematical properties such as convexity of the minimum-variance surface and nondominance of points, heuristically demonstrating different tangent planes instead of a unique tangent line. It serves as a theoretical stepping stone.

Unofficial AI-generated summary based on the public title and abstract. Not an official translation.

📝 gxceed 編集解説 — Why this matters

日本のGX文脈において

日本ではカーボン・クレジット市場の創設やGX投資促進が進む中、炭素オフセット投資の理論的枠組みは投資家のポートフォリオ構築に示唆を与える。ただし、実証や実務適用が未熟であり、今後の研究発展が待たれる。

In the global GX context

Globally, as carbon markets expand and transition finance grows, theoretical models linking carbon offsets to portfolio optimization are relevant. This paper extends classical CAPM to a multi-objective setting, offering a foundation for future empirical work and practical applications in climate finance.

👥 読者別の含意

🔬研究者:Provides a theoretical foundation for multi-objective portfolio optimization in carbon offset investments, useful for further research.

📄 Abstract（原文）

Our environment deteriorates primarily due to the emissions of carbon dioxide. Scientists and entrepreneurs promote carbon offset to reduce the emissions. Scientists and investors explore the investments of carbon offset. Some scientists encouragingly construct portfolio selection models but do not completely optimize them. Some scientists encouragingly construct capital asset pricing models (CAPM) but do not completely justify them. Under such contexts, this paper proposes a model of multiple-objective portfolio selection (MOPS) and preliminarily explores multiple-objective capital asset pricing models (MOCAPM). By the classical transition from portfolio selection to CAPM, we introductorily conjecture the extended transition from MOPS to MOCAPM. Specifically, we prove mathematical properties for the model. For instance, its minimum-variance surface is convex, and its feasible region is bounded by the convex surface. We examine whether a point on the minimum-variance surface is nondominated. By the properties, we heuristically prove different tangent planes for MOCAPM (instead of the unique tangent line for CAPM). We tentatively hint the conditions for a unique tangent plane. This paper acts as a footstep of the introductory conjecture.

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