Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions

المؤلفون المشاركون

Rong, Xi-min
Zhao, Hui
Sheng, De-Lei

المصدر

Abstract and Applied Analysis

العدد

المجلد 2014، العدد 2014 (31 ديسمبر/كانون الأول 2014)، ص ص. 1-19، 19ص.

الناشر

Hindawi Publishing Corporation

تاريخ النشر

2014-07-24

دولة النشر

مصر

عدد الصفحات

19

التخصصات الرئيسية

الرياضيات

الملخص EN

This paper investigates the excess-of-loss reinsurance and investment problem for a compound Poisson jump-diffusion risk process, with the risk asset price modeled by a constant elasticity of variance (CEV) model.

It aims at obtaining the explicit optimal control strategy and the optimal value function.

Applying stochastic control technique of jump diffusion, a Hamilton-Jacobi-Bellman (HJB) equation is established.

Moreover, we show that a closed-form solution for the HJB equation can be found by maximizing the insurer’s exponential utility of terminal wealth with the independence of two Brownian motions W ( t ) and W 1 ( t ) .

A verification theorem is also proved to verify that the solution of HJB equation is indeed a solution of this optimal control problem.

Then, we quantitatively analyze the effect of different parameter impacts on optimal control strategy and the optimal value function, which show that optimal control strategy is decreasing with the initial wealth x and decreasing with the volatility rate of risk asset price.

However, the optimal value function V ( t ; x ; s ) is increasing with the appreciation rate μ of risk asset.

نمط استشهاد جمعية علماء النفس الأمريكية (APA)

Sheng, De-Lei& Rong, Xi-min& Zhao, Hui. 2014. Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-19.
https://search.emarefa.net/detail/BIM-1033601

نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)

Sheng, De-Lei…[et al.]. Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions. Abstract and Applied Analysis No. 2014 (2014), pp.1-19.
https://search.emarefa.net/detail/BIM-1033601

نمط استشهاد الجمعية الطبية الأمريكية (AMA)

Sheng, De-Lei& Rong, Xi-min& Zhao, Hui. Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-19.
https://search.emarefa.net/detail/BIM-1033601

نوع البيانات

مقالات

لغة النص

الإنجليزية

الملاحظات

Includes bibliographical references

رقم السجل

BIM-1033601