Minimal Cost of a Brownian Risk without Ruin
AbstractIn this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The objective is to find the optimal reinsurance and cash injection strategy that minimizes the total cost to keep the company's surplus process non-negative, i.e. without ruin, where the cost function is defined as the total discounted value of the injections. The optimal solution is found explicitly by solving the according quasi-variational inequalities (QVIs).
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1112.4005.
Date of creation: Dec 2011
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-03 (All new papers)
- NEP-RMG-2012-01-03 (Risk Management)
- NEP-UPT-2012-01-03 (Utility Models & Prospect Theory)
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- Abel Cadenillas & Fernando Zapatero, 2000. "Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 141-156.
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