Exact solution of the ruin problem in the Cramér--Lundberg model with proportional investment
arXiv:2604.08745
Abstract
The Cramér-Lundberg model with exponential claims and proportional investment is solved exactly: the integro-differential equation for the survival probability reduces to a doubly confluent Heun equation, yielding an explicit solution in terms of Heun functions, a verification theorem, and a qualitative analysis of ruin probability versus investment share.