Optimal Reinsurance via Dirac-Feynman Approach

Muhsin Tamturk,Sergey Utev

doi:10.1007/s11009-018-9674-8

Muhsin Tamturk, Sergey Utev

Open Access

https://doi.org/10.1007/s11009-018-9674-8

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Abstract

In this paper, the Dirac-Feynman path calculation approach is applied to analyse finite time ruin probability of a surplus process exposed to reinsurance by capital injections. Several reinsurance optimization problems on optimum insurance and reinsurance premium with respect to retention level are investigated and numerically illustrated. The retention level is chosen to decrease the finite time ruin probability and to guarantee that reinsurance premium covers an average of overall capital injections. All computations are based on Dirac-Feynman path calculation approach applied to the convolution type operators perturbed by Injection operator (shift type operator). In addition, the effect of the Injection operator on ruin probability is analysed.

Highlights

The paper considers the application of the Quantum mechanic technique to compute the ruin probability of modified surplus process with reinsurance and the optimal reinsurance
We consider the following reinsurance agreement motivated by Nie et al (2011, 2015): the insured companies pay reinsurance premium in advance in order to get capital injections
All the methods have a main objective on the one hand to decrease the finite time ruin probability and on the other hand, to guarantee that reinsurance premium covers an average of overall capital injections

Summary

Introduction

The paper considers the application of the Quantum mechanic technique to compute the ruin probability of modified surplus process with reinsurance and the optimal reinsurance. Reinsurance is a risk sharing arrangement between a primary insurer and a reinsurer. There are different types of reinsurance agreements and various optimality approaches to reinsurance such as Castaner et al (2013), Denuit and Vermandele (1998), Dickson and Waters (1996), Schmidli (2002), Zhou and Yuen (2012). We consider the following reinsurance agreement motivated by Nie et al (2011, 2015): the insured companies pay reinsurance premium in advance in order to get capital injections

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