Proportional reinsurance and investment in multiple risky assets under borrowing constraint

In this paper, we consider the ruin probability minimization of an insurance company that buys proportional reinsurance and invests in markets where borrowing is constrained. We use a diffusion approximation model for the surplus process of this company and assume that the company invests its surplus into a riskless and multiple risk assets that are modeled as geometric Brownian motions. To find the results, we introduce an auxiliary market parametrized with fictitious processes to relax the borrowing constraint and apply the techniques of stochastic optimal control. In this way, we find the optimal proportional reinsurance and investment strategy of an insurance company investing into multiple risky assets to minimize its ruin probability under the borrowing constraint. Furthermore, from our solutions, we show how our results connect to economic survival analysis and how investment and reinsurance strategies are related.