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arXiv · 2604.08745

Exact solution of the ruin problem in the Cram\'er--Lundberg model with proportional investment

Platon Promyslov·Maxim Romanov·Goluba Yurieva
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Abstract

The Cram\'er-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.

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Platon Promyslov, Maxim Romanov, Goluba Yurieva. 2026-04-09. Exact solution of the ruin problem in the Cram\'er--Lundberg model with proportional investment. https://arxiv.org/abs/2604.08745

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