On Proportional Reinsurance With A Linear Transaction Rate
exponential utility, HJB equation, linear transaction rate, proportional reinsurance, Ruin probability
Risk and Decision Analysis
We study a model of an insurance company whose surplus is represented by a pure diffusion. The company is allowed to buy proportional reinsurance and invest its surplus in a Black-Sholes financial market. Further, it is assumed that transaction cost rate of the reinsurance decreases linearly while the insurance company buys more reinsurance. We consider two optimization criteria - minimizing probability of ruin and maximizing expected exponential utility of terminal wealth for a fixed time. Corresponding Hamilton-Jacobi-Bellman (HJB) equations are analyzed; consequently we find explicit expressions of the minimal ruin probability, maximal expected terminal utility, and their associated optimal reinsurance-investment strategies via various parameter conditions. We observe from the explicit results that for some special parameter cases, the optimal investment-reinsurance strategies coincide under the two optimization criteria; i.e., Ferguson's longstanding conjecture on the relation between the two problems holds. © 2012 - IOS Press and the authors. All rights reserved.
Department of Mathematics
Original Publication Date
DOI of published version
Luo, Shangzhen, "On Proportional Reinsurance With A Linear Transaction Rate" (2012). Faculty Publications. 1821.