Optimal control of capital injections by reinsurance in a diffusion approximation

2009 ◽  
Vol 30 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Julia Eisenberg ◽  
Hanspeter Schmidli
Keyword(s):  
Optimal Control ◽  
Diffusion Approximation ◽  
Capital Injections

scholarly journals Optimal Control of Capital Injections by Reinsurance with a Constant Rate of Interest

2011 ◽  
Vol 48 (3) ◽  
pp. 733-748 ◽  
Author(s):  
Julia Eisenberg ◽  
Hanspeter Schmidli
Keyword(s):  
Diffusion Approximation ◽  
Value Function ◽  
Risk Model ◽  
Classical Risk Model ◽  
Surplus Process ◽  
The Individual ◽  
Reinsurance Treaty ◽  
Riskless Asset ◽  
Capital Injections ◽  
The Value Function

We consider a classical risk model and its diffusion approximation, where the individual claims are reinsured by a reinsurance treaty with deductible b ∈ [0, b̃]. Here b = b̃ means ‘no reinsurance’ and b= 0 means ‘full reinsurance’. In addition, the insurer is allowed to invest in a riskless asset with some constant interest rate m > 0. The cedent can choose an adapted reinsurance strategy {bt}t≥0, i.e. the parameter can be changed continuously. If the surplus process becomes negative, the cedent has to inject additional capital. Our aim is to minimise the expected discounted capital injections over all admissible reinsurance strategies. We find an explicit expression for the value function and the optimal strategy using the Hamilton-Jacobi-Bellman approach in the case of a diffusion approximation. In the case of the classical risk model, we show the existence of a ‘weak’ solution and calculate the value function numerically.

scholarly journals Optimal Control of Capital Injections by Reinsurance with a Constant Rate of Interest

2011 ◽  
Vol 48 (03) ◽  
pp. 733-748
Author(s):  
Julia Eisenberg ◽  
Hanspeter Schmidli
Keyword(s):  
Diffusion Approximation ◽  
Value Function ◽  
Risk Model ◽  
Classical Risk Model ◽  
Surplus Process ◽  
The Individual ◽  
Reinsurance Treaty ◽  
Riskless Asset ◽  
Capital Injections ◽  
The Value Function

We consider a classical risk model and its diffusion approximation, where the individual claims are reinsured by a reinsurance treaty with deductible b ∈ [0, b̃]. Here b = b̃ means ‘no reinsurance’ and b= 0 means ‘full reinsurance’. In addition, the insurer is allowed to invest in a riskless asset with some constant interest rate m > 0. The cedent can choose an adapted reinsurance strategy {b t } t≥0, i.e. the parameter can be changed continuously. If the surplus process becomes negative, the cedent has to inject additional capital. Our aim is to minimise the expected discounted capital injections over all admissible reinsurance strategies. We find an explicit expression for the value function and the optimal strategy using the Hamilton-Jacobi-Bellman approach in the case of a diffusion approximation. In the case of the classical risk model, we show the existence of a ‘weak’ solution and calculate the value function numerically.

scholarly journals On optimal control of capital injections by reinsurance and investments

2010 ◽  
Vol 31 (2) ◽  
pp. 329-345 ◽  
Author(s):  
Julia Eisenberg
Keyword(s):  
Optimal Control ◽  
Capital Injections
Sign in / Sign up

Export Citation Format

Share Document