حل معادله انتگرال دیفرانسیل جزئی مربوط به ریسک عملیاتی با بکارگیری روش تفاضلات متناهی

نویسندگان
1 دانشگاه آزاد اسلامی، واحد تهران مرکزی
2 دانشگاه آزاد اسلامی، واحد شهر ری
چکیده
ریسک عملیاتی یکی از ریسک‌های شناسایی شده در سازمان‌ها بالاخص در بانک‌ها است و کمیته‌های نظارت بانکی توجه ویژه‌ای به آن دارند. در این مقاله مدل ریاضی بر اساس مدل پیشرفته ریسک عملیاتی برای محاسبه احتمال بقای بانک به صورت یک معادله انتگرال دیفرانسیل جزئی ولترا در نظر گرفته شده است. این معادله با به کارگیری روش تفاضلات متناهی با قاعده ذوزنقه‌ای جهت تخمین بخش انتگرالی آن به صورت عددی حل و تاثیر تغییر پارامترهای مدل بر خروجی مساله بررسی شده است. علاوه بر این، پایداری و همگرایی روش، مورد بحث قرار گرفته و نتایج عددی آن ارائه شده است.
کلیدواژه‌ها

عنوان مقاله English

Solving partial integro-differential equation related to operational risk by applying the finite differences method

نویسندگان English

Mansoorehli Rasooli 1
Mohammad Ali Fariborzi Araghi 1
Tayebeh Damercheli 2
1 Islamic Azad university, Central Tehran branch
2 Islamic Azad university, Shahre-Rey branch
چکیده English

Operational risk is one of the identified risks in organizations, especially in banks, and Basel committees on banking supervision pay special attention to it. In this paper, the mathematical model based on the advanced operational risk model is considered to calculate the probability of survive as a partial Volterra integro-differentail equation. This equation has been solved numerically by applying the finite differences method with trapezoidal rule to estimate its integral part and the effect of changing the model parameters on the output of the problem has been investigated. In addition, the stability and convergence of the method are discussed and its numerical results are presented.

کلیدواژه‌ها English

Operational risk
partial integro-differential equation
Finite differences
Stability
Convergence
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